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Main  Building,  Armour  Institute  of  Technology 


CYCLOPEDIA  OF 
DRAWING 

MECHANICAL  DRAWING 

By  Ervin  Kenison,  S.  B. 

Department  of  Mechanical  Drawing, 

Massachusetts  Institute  of  Technology. 

SHADES  AND  SHADOWS 

By  Harry  W.  Gardner,  S.  B. 

Assistant  Professor  of  Architecture, 

Massachusetts  Institute  of  Technology. 

PERSPECTIVE  DRAWING 

By  William  H.  Lawrence,  S.  B. 

Associate  Professor  of  Architecture, 

Massachusetts  Institute  of  Technology. 

FREEHAND  DRAWING 

By  Herbert  E.  Everett 
Department  of  Architecture, 

University  of  Pennsylvania. 

PEN  AND  INK  RENDERING 

By  David  A.  Gregg 
Department  of  Architecture, 

Massachusetts  Institute  of  Technology. 

RENDERING  IN  WASH 

By  Herman  V.  von  Holst,  A.  B.,  S.  B. 

Architect,  Chicago 

ARCHITECTURAL  LETTERING 

By  Frank  Chouteau  Brown. 

Architect,  Boston 

Compiled  from  the  Instruction  Papers  in  the 
Architectural  Course  of  the  American  School  of 
Correspondence  at  Armour  Institute  of  Tech- 
nology  ::::::::::::::  Chicago , Illinois 

Edited  by 

ALFRED  E.  ZAPF,  S.  B. 

Secretary  American  School  of  Correspondence 


Copyright  1 005  by 
American  School  of  Corresiondence 

Entered  at  Stationers'  Hall , London 
All  Rights  Reserved 


y 


THIS  VOLUME  CONSISTS  OF  NINE  OF  THE  FIFTY 
REGULAR  INSTRUCTION  PAPERS  IN  THE  ARCHITECT- 
URAL COURSE  OF  THE  AMERICAN  SCHOOL  OF  CORRES- 
PONDENCE, INDEXED  AND  BOUND  TOGETHER  IN  CON- 
VENIENT FORM  FOR  READY  REFERENCE,  BUT  NOT  IN  THE 
ORDER  USUALLY  STUDIED. 

THE  INSTRUCTION  PAPERS  OF  THE  AMERICAN 
SCHOOL  OF  CORRESPONDENCE  ARE  PREPARED  EXCLU- 
SIVELY FOR  THE  USE  OF  ITS  STUDENTS  BY  MEN  OF 
ACKNOWLEDGED  PROFESSIONAL  STANDING,  AND  REPRE- 
SENT YEARS  OF  SPECIAL  PREPARATION  NECESSARY  TO 
ADAPT  THEM  TO  THE  NEEDS  OF  PERSONS  OBLIGED 
TO  STUDY  WITHOUT  THE  DIRECT  ASSISTANCE  OF  A 
PERSONAL  TEACHER. 

THE  CHIEF  AIM  OF  THIS  WORK  IS  TO  ACQUAINT  THE 
PUBLIC  WITH  THE  STANDARD,  SCOPE,  AND  PRACTICAL 
VALUE  OF  THESE  PAPERS  THROUGH  AN  OPPORTUNITY 
FOR  PERSONAL  EXAMINATION;  AND  IT  IS  HOPED  THAT 
SUFFICIENT  MATERIAL  IS  GIVEN  HERE  TO  AROUSE  IN 
THE  READER  A DESIRE  TO  KNOW  MORE. 

ALTHOUGH  PUBLISHED  PRIMARILY  TO  SHOW  THE 
CHARACTER  OF  THE  INSTRUCTION  OFFERED  BY  THE 
AMERICAN  SCHOOL  OF  CORRESPONDENCE,  AND  REPRE- 
SENTING ONLY  A SMALL  PORTION  OF  THE  COMPLETE 
COURSE,  IT  IS  CONFIDE NTI  Y BELIEVED  THAT  THIS  VOL- 
UME HAS  IN  ITSELF  ENOUGH  CONDENSED,  PRACTICAL 
INFORMATION  TO  MAKE  IT  OF  IMMEDIATE  VALUE  TO  THE 
DRAFTSMAN,  STUDENT,  OR  TEACHER. 


EXAMINATION  QUESTIONS 


FOLLOWING  EACH  SECTION  ARE  THE  QUES 
TIONS  OR  PLATES  WHICH  CONSTITUTE  THE 
REGULAR  EXAMINATION  OF  THE  AMERICAN 
SCHOOL  OF  CORRESPONDENCE.  THEY  OFFER 
THE  READER  A MEANS  OF  TESTING  HIS 
KNOWLEDGE  OF  THE  SUBJECTS  TREATED. 

INABILITY  TO  ANSWER  THESE  QUESTIONS, 
OR  TO  SOLVE  THE  PROBLEMS,  WILL  SERVE  TO 
SHOW  THE  NECESSITY  FOR  FURTHER  STUDY. 

THE  READER  IS  URGED  TO  SOLVE  EVERY 
PROBLEM,  CHECKING  HIS  RESULTS  WHEREVER 
POSSIBLE  WITH  SIMILAR  PROBLEMS  IN  THE 
PRECEDING  PAGES.  THIS  WILL  AFFORD  AN  EX- 
CELLENT MEANS  FOR  FIXING  THE  MATTER  IN 
HIS  MIND. 

STUDENTS  PREPARING  FOR  COLLEGE  OR 
CIVIL  SERVICE  EXAMINATIONS  WILL  FIND 
THESE  QUESTIONS  OF  GREAT  VALUE 


FRAGMENTS  FROM  ROMAN  TEMPLE  AT  CORI,  ITALY. 

One  of  the  most  interesting  examples  of  architectural  rendering  in  existence. 

Original  drawing  by  Emanuel  Brune. 

Reproduced  by  permission  of  Massachusetts  Institute  of  Technology . 


MECHANICAL  DRAWING* 


The  subject  of  mechanical  drawing  is  of  great  interest  and 
importance  to  all  mechanics  and  engineers.  Drawing  is  the 
method  used  to  show  graphically  the  small  details  of  machinery; 
it  is  the  language  by  which  the  designer  speaks  to  the  workman; 
it  is  the  most  graphical  way  to  place  ideas  and  calculations  on 
record.  Working  drawings  take  the  place  of  lengthy  explana- 
tions, either  written  or  verbal.  A brief  inspection  of  an  accurate, 
well-executed  drawing  gives  a better  idea  of  a machine  than  a 
large  amount  of  verbal  description.  The  better  and  more  clearly 
a drawing  is  made,  the  more  intelligently  the  workman  can  com- 
prehend the  ideas  of  the  designer.  A thorough  training  in  this 
important  subject  is  necessary  to  the  success  of  everyone  engaged 
in  mechanical  work.  The  success  of  a draftsman  depends  to  some 
extent  upon  the  quality  of  his  instruments  and  materials.  Begin- 
ners frequently  purchase  a cheap  grade  of  instruments.  After 
they  have  become  expert  and  have  learned  to  take  care  of  their 
instruments  they  discard  them  for  those  of  better  construction  and 
finish.  This  plan  has  its  advantages,  but  to  do  the  best  work, 
strong,  well-made  and  finely  finished  instruments  are  necessary. 

INSTRUflENTS  AND  HATERIALS. 

Drawing  Paper.  In  selecting  drawing  paper,  the  first  thing 
to  be  considered  is  the  kind  of  paper  most  suitable  for  the  pro- 
posed work.  For  shop  drawings,  a manilla  paper  is  frequently 
used,  on  account  of  its  toughness  and  strength,  because  the  draw- 
ing is  likely  to  be  subjected  to  considerable  hard  usage.  If  a 
finished  drawing  is  to  be  made,  the  best  white  drawing  paper 
should  be  obtained,  so  that  the  drawing  will  not  fade  or  become 
discolored  with  age.  A good  drawing  paper  should  be  strong, 
have  uniform  thickness  and  surface,  should  stretch  evenly,  and 
should  neither  repel  nor  absorb  liquids.  It  should  also  allow  con- 
siderable erasing  without  spoiling  the  surface,  and  it  should  lie 
smooth  when  stretched  or  when  ink  or  colors  are  used.  It  is,  of 


7 


4 


MECHANICAL  DRAWING. 


course,  impossible  to  find  all  of  these  qualities  in  any  one  paper, 
as  for  instance  great  strength,  cannot  be  combined  with  fine 
surface. 

In  selecting  a drawing  paper  the  kind  should  be  chosen 
which  combines  the  greatest  number  of  these  qualities  for  the 
given  work  Of  the  better  class  Whatman’s  are  considered  by 
far  the  best.  This  paper  is  made  in  three  grades;  the  hot 
'pressed  has  a smooth  surface  and  is  especially  adapted  for  pencil 
and  very  fine  line  drawing,  the  cold  pressed  is  rougher  than 
the  hot  pressed,  has  a finely  grained  surface  and  is  more  suit- 
able for  water  color  drawing  ; the  rough  is  used  for  tinting.  The 
cold  pressed  does  not  take  ink  as  well  as  the  hot  pressed,  but 
erasures  do  not  show  as  much  on  it,  and  it  is  better  for  general 
work.  There  is  but  little  difference  in  the  two  sides  of  Whatman’s 
paper,  and  either  can  be  used.  This  paper  comes  in  sheets  of 
standard  sizes  as  follows:  — 


Cap, 

Demy, 

Medium, 

Royal, 

Super-Royal, 
Imperi  al, 


13  X 17  inches. 
15  X 20  “ 

17  X 22  “ 

19  X 24  “ 

19X27  “ 

22  X 30  “ 


Elephant, 

Columbia, 

Atlas, 

Double  Elephant, 

Antiquarian, 

Emperor, 


23  X 28  inches. 
23  X 34  “ 

26  X 34  “ 

27  X 40  “ 

31  X 53  “ 

48  X 68  “ 


The  usual  method  of  fasteningpaper  to  a drawing  board  is  by 
means  of  thumb  tacks  or  small  one-ounce  copper  or  iron  tacks. 
In  fastening  the  paper  by  this  method  first  fasten  the  upper  left 
hand  corner  and  then  the  lower  right  pulling  the  paper  taut.  The 
other  two  corners  are  then  fastened,  and  sufficient  number  of  tacks 
are  placed  along  the  edges  to  make  the  paper  lie  smoothly.  For 
very  fine  work  the  paper  is  usually  stretched  and  glued  to  the 
board.  To  do  this  the  edges  of  the  paper  are  first  turned  up  all 
the  way  round,  the  margin  being  at  least  one  inch.  The  whole 
surface  of  the  paper  included  between  these  turned  up  edges  is 
then  moistened  by  means  of  a sponge  or  soft  cloth  and  paste  or 
glue  is  spread  on  the  turned  up  edges.  After  removing  all  the 
surplus  water  on  the  paper,  the  edges  are  pressed  down  on  the 
board,  commencing  at  one  corner.  During  this  process  of  laying 
down  the  edges,  the  paper  should  be  stretched  slightly  by  pulling 
the  edges  towards  the  edges  of  the  drawing  board.  The  drawing 
board  is  then  placed  horizontally  and  left  to  dry.  After  the*paper 
has  become  dry  it  will  be  found  to  be  as  smooth  and  tight  as  a 


MECHANICAL  DRAWING. 


5 


drum  head.  If,  in  stretching,  the  paper  is  stretched  too  much  it 
is  likely  to  split  in  drying.  A slight  stretch  is  sufficient. 

Drawing  Board.  The  size  of  the  drawing  board  depends 
upon  the  size  of  paper.  Many  draftsmen,  however,  have  several 
boards  of  various  sizes,  as  they  are  very  convenient.  The  draw- 
ing board  is  usually  made  of  soft  pine,  which  should  be  well  sea- 
soned and  straight  grained.  The  grain  should  run  lengthwise  of 
the  board,  and  at  the  two  ends  there  should  be  pieces  about  1 J or 
2 inches  wide  fastened  to  the  board  by  nails  or  screws.  These 
end  pieces  should  be  perfectly  straight  for  accuracy  in  using  the 
T-square.  Frequently  the  end  pieces  are  fastened  by  a glued 


matched  joint,  nails  and  screws  being  also  used.  Two  cleats  on 
the  bottom  extending  the  whole  width  of  the  board,  will  reduce 
the  tendency  to  warp,  and  make  the  board  easier  to  move  as  they 
raise  it  from  the  table. 

Thumb  Tacks.  Thumb  tacks  are  used  for  fastening  the 
paper  to  the  drawing  board.  They  are  usually  made  of  steel 
either  pressed  into  shape,  as  in  the  cheaper  grades,  or  made  with  a 
head  of  German  silver  with  the  point  screwed  and  riveted  to  it. 
They  are  made  in  various  sizes  and  are  very  convenient  as  they 
can  be  easily  removed  from  the  board.  For  most  work  however, 


9 


6 


MECHANICAL  DRAWING. 


draftsmen  use  small  one-ounce  copper  or  iron  tacks,  as  they  can  be 
forced  flush  with  the  drawing  paper,  thus  offering  no  obstruction 
to  the  T-square.  They  also  possess  the  advantage  of  cheapness. 

Pencils.  In  pencilling  a drawing  the  lines  should  be  very 
fine  and  light.  To  obtain  these  light  lines  a hard  lead,  pencil  must 
be  used.  Lead  pencils  are  graded  according  to  their  hardness, 
and  are  numbered  by  using  the  letter  H.  In  general  a lead  pencil 
of  5H  (or  HHHHH)  or  6H  should  be  used.  A softer  pencil,  4H, 

is  better  for  making  letters,  figures  and 
points.  A hard  lead  pencil  should  be 
sharpened  as  shown  in  Fig.  1.  The  wood 
is  cut  away  so  that  about  i or  | inch 
of  lead  projects.  The  lead  can  then  be 
|rb|  sharpened  to  a chisel  edge  by  rubbing  it 
I If  against  a bit  of  sand  paper  or  a fine  file. 
I I It  should  be  ground  to  a chisel  edge  and 
I/  the  comers  slightly  rounded.  In  making 
the  straight  lines  the  chisel  edge  should 
be  used  by  placing  it  against  the  T-square 
or  triangle,  and  because  of  the  chisel  edge 
the  lead  will  remain  sharp  much  longer  than  if  sharpened  to  a point. 
This  chisel  edge  enables  the  draftsman  to  draw  a fine  line  exactly 
through  a given  point.  If  the  drawing  is  not  to  be  inked,  but  is 
made  for  tracing  or  for  rough  usage  in  the  shop,  a softer  pencil, 
3H  or  4H,  may  be  used,  as  the  lines  will  then  be  somewhat  thicker 
and  heavier.  The  lead  for  compasses  may  also  be  sharpened  to  a 
point  although  some  draftsmen  prefer  to  use  a chisel  edge  in  the 
compasses  as  well  as  for  the  pencil. 

In  using  a very  hard  lead  pencil,  the  chisel  edge  will  make  a 
deep  depression  in  the  paper  if  much  pressure  is  put  on  the  pencil. 
As  this  depression  cannot  be  erased  it  is  much  better  to  press 
lightly  on  the  pencil. 

Erasers.  In  making  drawings,  but  little  erasing  should  be 
necessary.  However,  in  case  this  is  necessary,  a soft  rubber 
should  be  used.  In  erasing  a line  or  letter,  great  care  must  be 
exercised  or  the  surrounding  work  will  also  become  erased.  To 
prevent  this,  some  draftsmen  cut  a slit  about  3 inches  long  and 
J to  ^ inch  wide  in  a card  as  shown  in  Fig.  2.  The  card  is  then 


10 


MECHANICAL  DRAWING. 


7 


placed  over  the  work  and  the  line  erased  without  erasing  the  rest 
of  the  drawing.  An  erasing  shield  of  a form  similar  to  that  shown 
in  Fig.  3 is  very  convenient,  especially  in  erasing  letters.  It  is 
made  of  thin  sheet  metal  and  is  clean  and  durable. 

For  cleaning  drawings,  a sponge  rubber  may  be  used.  Bread 


C 


Fig.  2. 


crumbs  are  also  used  for  this  purpose.  To  clean  the  drawing 
scatter  dry  bread  crumbs  over  it  and  rub  them  on  the  surface 
with  the  hand. 

T-Square.  The  T-square  consists  of  a thin  straight  edge 


Fig.  4. 


called  the  blade,  fastened  to  a head  at  right  angles  to  it.  It  gets 
its  name  from  the  general  shape.  T-squares  are  made  of  various 
materials,  wood  being  the  most  commonly  used.  Fig.  4 shows  an 
ordinary  form  of  T-square  which  is  adapted  to  most  work.  In 
Fig.  5 is  shown  a T-square  with  edges  made  of  ebony  or  mahogany, 
as  these  woods  are  much  harder  than  pear  wood  or  maple,  which 
is  generally  used.  The  head  is  formed  so  as  to  fit  against  the  left- 
hand  edge  of  the  drawing  board,  while  the  blade  extends  over  the 
surface.  It  is  desirable  to  have  the  blade  of  the  T-square  form  a 
right  angle  with  the  head,  so  that  the  lines  drawn  with  the  T- 
square  will  be  at  right  angles  to  the  left-hand  edge  of  the  board. 
This,  however,  is  not  absolutely  necessary,  because  the  lines  drawn 
with  the  T-square  are  always  with  reference  to  one  edge  of  the 


ll 


8 


MECHANICAL  DRAWING. 


board  only,  and  if  this  edge  of  the  board  is  straight,  the  lines 
drawn  with  the  T-square  will  be  parallel  to  each  other.  The  T- 
square  should  never  be  used  except  with  the  left-hand  edge  of  the 
board,  as  it  is  almost  impossible  to  find  a drawing  broad  with  the 
edges  parallel  or  at  right  angles  to  each  other. 

The  T-square  with  an  adjustable  head  is  frequently  very  con- 
venient, as  it  is  sometimes  necessary  to  draw  lines  parallel  to  each 


Fig.  5. 


other  which  are  not  at  right  angles  to  the  left-hand  edge  of  the 
board.  This  form  of  T-square  is  similar  to  the  ordinary  T-square 
already  described,  but  the  head  is  swiveled  so  that  it  may  be 
clamped  at  any  desired  angle.  The  ordinary  T-square  as  shown 

in  Figs.  4 and  5 is,  how 
ever,  adapted  to  almost 
any  class  of  drawing. 

Fig.  6 shows  the 
method  of  drawing  parallel 
horizontal  lines  with  the 
T-square.  With  the  head 
of  the  T-square  in  contact 
with  the  left-hand  edge  of 
the  board,  the  lines  may  be 
drawn  by  moving  the  T-square  to  the  desired  position.  In  using  the 
T-square  the  upper  edge  should  always  be  used  for  drawing  as  the 
two  edges  may  not  be  exactly  parallel  and  straight,  and  also  it  is 
more  convenient  to  use  this  edge  with  the  triangles.  If  it  is  neces- 
sary  to  use  a straight  edge  for  trimming  drawings  or  cutting  the 
paper  from  the  board,  the  lower  edge  of  the  T-square  should  be 
used  so  that  the  upper  edge  may  not  be  marred. 

For  accurate  work  it  is  absolutely  necessary  that  the  working 
edge  of  the  T-square  should  be  exactly  straight.  To  test  the 


Fig.  6. 


12 


MECHANICAL  DRAWING. 


9 


straightness  of  the  edge  of  the  T-square,  two  T-squares  may  be 
placed  together  as  shown  in  Fig.  7.  This  figure  shows  plainly 
that  the  edge  of  one  of  the  T-squares  is  crooked.  This  fact,  how- 
ever, does  not  prove  that  either  one  is  straight,  and  for  this  deter- 
mination a third  blade  must  be 
used  and  tried  with  the  two 
given  T-squares  successively. 

Triangles.  Triangles  are 
made  of  various  substances  such 
as  wood,  rubber,  celluloid  and 
steel.  Wooden  triangles  are 
cheap  but  are  likely  to  warp  and  get  out  of  shape.  The  rubber  tri- 
angles are  frequently  used,  and  are  in  general  satisfactory.  The 
transparent  celluloid  triangle  is,  however,  extensively  used  on  ac- 
count of  its  transparency,  which  enables  the  draftsmen  to  see  the 
work  already  done  even  when  covered  with  the  triangle.  In  using 
a rubber  or  celluloid  triangle  take  care  that  it  lies  perfectly  flat  or 


is  hung  up  when  not  in  use  ; when  allowed  to  lie  on  the  drawing 
board  with  a pencil  or  an  eraser  under  one  corner  it  will  become 
warped  in  a short  time,  especially  if  the  room  is  hot  or  the  sun 
happens  to  strike  the  triangle. 

Triangles  are  made  in  various  sizes,  and  many  draftsmen 
have  several  constantly  on  hand.  A triangle  from  6 to  8 inches 
on  a side  will  be  found  convenient  for  most  work,  although  there 
are  many  cases  where  a small  triangle  measuring  about  4 inches 


13 


10 


MECHANICAL  DRAWING. 


on  a side  will  be  found  useful.  Two  triangles  are  necessary  for 
every  draftsman,  one  having  two  angles  of  45  degrees  each  and 
one  a right  angle  ; and  the  other  having  one  angle  of  60  degrees, 
one  of  30  degrees  and  one  of  90  degrees. 

The  value  of  the  triangle  depends  upon  the  accuracy  of  the 
angles  and  the  straightness  of  the  edges.  To  test  the  accuracy  of 

the  right  angle  of  a tri- 
angle, place  the  triangle 
with  the  lower  edge  rest- 
ing on  the  edge  of  the 
T-square,  as  shown  in 
Fig.  8.  Now  draw  the 
line  C D,  which  should  be 
perpendicular  to  the  edge 
of  the  T-square.  The 
same  triaaigle  should  then 
be  placed  in  the  position  shown  at  B.  If  the  right  angle  of  the 
triangle  is  exactly  90  degrees  the  left-hand  edge  of  the  triangle 
should  exactly  coincide  with  the  line  C D. 

To  test  the  accuracy  of  the  45-degree  triangles,  first  test  the 
right  angle  then  place  the 
triangle  with  the  lower 
edge  resting  on  the  work- 
ing edge  of  the  T-square, 
and  draw  the  line  E F as 
shown  in  Fig.  9.  Now 
without  moving  the  T- 
square  place  the  triangle 
so  that  the  other  45-degree 
angle  is  in  the  position 
occupied  by  the  first.  If  the  two  45-degree  angles  coincide  th&y 
are  accurate. 


Triangles  are  very  convenient  in  drawing  lines  at  right 
angles  to  the  T-square.  The  method  of  doing  this  is  shown  in 
Fig.  10.  Triangles  are  also  used  in  drawing  lines  at  an  angle 
with  the  horizontal,  by  placing  them  on  the  board  as  shown  in 
big.  11.  Suppose  the  line  E F (Fig.  12)  is  drawn  at  any  angle, 
and  we  wish  to  draw  a line  through  the  point  P parallel  to  it. 


14 


* — i~2- — i 


A TYPICAL  ARCHITECT’S  DRAWING. 

This  shows  the  conventional  manner  of  indicating  the  over-all  dimensions  of  the  house,  the  size 
and  shape  of  the  rooms,  the  finish,  the  location  of  light  and  other  fixtures,  the 
swing  of  the  doors,  etc. ; also  the  conventional  style  of  lettering. 


MECHANICAL  DRAWING. 


11 


First  place  one  of  the  triangles  as  shown  at  A,  having  one  edge 
coinciding  with  the  given  line.  Now  take  the  other  triangle  and 
place  one  of  its  edges  in  contact  with  the  bottom  edge  of  triangle 
A.  I [olding  the  triangle  B firmly  with  the  left  hand  the  triangle 
A may  be  slipped  along  to  the  right  or  to  the  left  until  the  edge 
of  the  triangle  reaches  the 
point  P.  The  line  M N 
may  then  be  drawn  along 
the  edge  of  the  triangle 
passing  through  the  point 
P.  In  place  of  the  tri- 
angle B any  straight  edge 
such  as  a T-square  may  be 
used. 


A line  can  be  drawn 

perpendicular  to  another  by  means  of  the  triangles  as  follows. 
Let  E F (Fig.  IB)  be  the  given  line,  and  suppose  we  wish  to 
draw  a line  perpendicular  to  E F through  the  point  D.  Place 
the  longest  side  of  one  of  the  triangles  so  that  it  coincides 

with  the  line  E F,  as  the 
triangle  is  shown  in  posi- 
tion at  A.  Place  the  other 
triangle  (or  any  straight 
edge)  in  the  position  of 
the  triangle  as  shown  at 
B,  one  edge  resting  against 
the  edge  of  the  triangle  A. 
Then  holding  B with  the 
left  hand,  place  the  tri- 
angle A in  the  position  shown  at  C,  so  that  the  longest  side 
passes  through  the  point  D.  A line  can  then  be  drawn  through 
the  point  D perpendicular  to  E F. 

In  previous  figures  we  have  seen  how  lines  may  be  drawn 
making  angles  of  30,  45,  GO  and  90  degrees  with  the  horizontal. 
If  it  is  desired  to  draw  lines  forming  angles  of  15  and  T5  degrees 
the  triangles  may  be  placed  as  shown  in  Fig.  14. 

In  using  the  triangles  and  T-square  almost  any  line  may  be 
drawn.  Suppose  we  wish  to  draw  a rectangle  having  one  side 


15 


12 


MECHANICAL  DRAWING. 


horizon tal.  First  place  the  T-square  as  shown  in  Fig.  15.  By 
moving  the  T-square  up  or  down,  the  sides  A B and  D C may  be 
drawn,  because  they  are  horizontal  and  parallel.  Now  place  one 
of  the  triangles  resting  on  the  T-square  as  shown  at  E,  and  hav- 
ing the  left-hand  edge  passing  through  the  point  D.  The  vertical 


line  D A may  be  drawn,  and  by  sliding  the  triangle  along  the  edge 
of  the  T-square  to  the  position  F the  line  B C may  be  drawn  by 
using  the  same  edge.  These  positions  are  shown  dotted  in  Fig.  15. 

If  the  rectangle  is  to  be  placed  in  some  other  position  on  the 
drawing  board,  as  shown  in  Fig.  1G,  place  the  45-degree  triangle 

F so  that  one  edge  is 
parallel  to  or  coincides 
with  the  side  D C.  Now 
holding  the  triangle  F in 
position  place  the  triangle 
H so  that  its  upper  edge 
coincides  with  the  lower 
edge  of  the  triangle  F, 
By  holding  H in  position 
and  sliding  the  triangle  F 
along  its  upper  edge,  the  sides  A B and  D C may  be  drawn. 
To  draw  the  sides  A I)  and  B C the  triangle  should  be  used  as 
shown  at  E. 

Compasses.  Compasses  are  used  for  drawing  circles  and 
arcs  of  circles.  They  are  made  of  various  materials  and  in  various 
sizes.  The  cheaper  class  of  instruments  are  made  of  brass,  but 
they  are  unsatisfactory  on  account  of  the  odor  and  the  tendency 
to  tarnish.  The  best  material  is  German  silver.  It  does  not  soil 


16 


MECHANICAL  DRAWING. 


18 


readily,  it  lias  no  odor,  and  is  easy  to  keep  clean.  Aluminum  in- 
struments possess  the  advantage  of  lightness,  hut  on  account  of 
the  soft  metal  they  do  not  wear  well. 

The  compasses  are  made  in  the  form  shown  in  Figs.  17  and 
18.  Pencil  and  pen  points  are  provided,  as  shown  in  Fig.  17. 
Either  pen  or  pencil  may  he  inserted  in  one  leg  by  means  of  a 
shank  and  socket.  The 
other  leg  is  fitted  with  a 
needle  point  which  is 
placed  at  the  center  of  the 
circle.  In  most  instru- 
ments the  needle  point  is 
separate,  and  is  made  of  a 
piece  of  round  steel  wire 
having  a square  shoulder 
at  one  or  both  ends.  Be- 
low this  shoulder  the  needle  point  projects.  The  needle  is 
made  in  this  form  so  that  the  hole  in  the  paper  may  he  very 
minute. 

In  some  instruments  lock  nuts  are  used  to  hold  the  joint 
firmly  in  position.  These  lock  nuts  are  thin  discs  of  steel,  with 

notches  for  using  a wrench  or 
forked  key.  Fig.  19  shows  the 
detail  of  the  joint  of  high  grade 
instruments.  Both  legs  are  alike 
at  the  joint,  and  two  pivoted 
screws  are  inserted  in  the  yoke. 
This  permits  ample  movement 
of  the  legs,  and  at  the  same 
time  gives  the  proper  stiff- 
ness. The  flat  surface  of  one  of 
the  legs  is  faced  with  steel,  the  other  being  of  German  silver, 
in  order  that  the  rubbing  parts  maybe  of  different  metals.  Small 
set  screws  are  used  to  prevent  the  pivoted  screws  from  turning 
in  the  yoke.  The  contact  surfaces  of  this  joint  are  made  cir« 
cular  to  exclude  dust  and  dirt  and  to  prevent  rusting  of  the 
steel  face. 

Figs.  20,  21,  and  22  show  the  detail  of  the  socket;  hi  some 


D 


T 

\ 

\ 

!\EN' 

L_A 


.N 


- — ‘C 


!\F\ 

L.N 


Fig.  15. 


17 


14 


MECHANICAL  DRAWING. 


r 


instruments  the  shank  and  socket  are  pentagonal,  as  shown  in 
Fig.  20.  The  shank  enters  the  socket  loosely,  and  is  held  in  place 
by  means  of  the  screw.  Unless  used  very  carefully  this  arrange- 
ment is  not  durable  because  the  sharp  corners  soon  wear,  and  the 
pressure  on  the  set  screw  is  not  sufficient  to  hold  the  shank  firmly 
in  place. 

In  Fig.  21  is  shown  another  form  of  shank.  This  is  round, 
having  a flat  top.  A set  screw  is  also  used  to  hold  this  in  posi- 
tion. A still  better  form  of  socket  is  shown  in  Fig*.  22 : the  hole 

O 


Fig.  17. 


is  made  tapered  and  is  circular.  The  shank  fits  accurately,  and 
is  held  in  perfect  alignment  by  a small  steel  key.  The  clamping 
screw  is  placed  upon  the  side,  and  keeps  the  two  portions  of  the 
split  socket  together. 

Figs.  17  and  18  show  that  both  legs  of  the  compasses  are 
jointed  in  order  that  the  lower  part  of  the  legs  may  be  perpen- 
dicular to  the  paper  while  drawing  circles.  In  this  way  the 
needle  point  makes  but  a small  hole  in  the  paper,  and  both  nibs  of 


18 


A beautiful  example  of  rendering  in  wash,  showing  conventional  method  of  representing 
plan  and  surrounding  grounds.  This  is  usually  done  in  strong  contrasting  colors. 
The  black  rectangles  indicate  statuary;  the  crossed  lines  arbors.  Note 
how  the  shadows  of  the  building,  terraces,  statuary,  etc. , help  to 
give  interest  to  the  drawing.  Contrast  this  plan  with 
the^  one  rendered  in  pen  and  ink  page  421. 

See  also  “Rendering  in  Wash’’  page  453. 


MECHANICAL  DRAWING. 


15 


the  pen  will  press  equally  on  the  paper.  In  pencilling  circles  it 
is  not  as  necessary  that  the  pencil  should  be  kept  vertical;  it  is  a 
good  plan,  however,  to  learn  to  use  them  in  this  way  both  in  pen- 
cilling* and  inking.  The  com- 
passes  should  be  held  loosely  be- 
tween the  thumb  and  forefinger. 

If  the  needle  point  is  sharp,  as 
it  should  be,  only  a slight  pres- 
sure will  be  required  to  keep  it 
in  place.  While  drawing  the 
circle,  incline  the  compasses 
slightly  in  the  direction  of 
revolution  and  press  lightly  on 
the  pencil  or  pen. 

In  removing  the  pencil  or 
pen,  it  should  be  pulled  out  Fi£-  19- 

straight.  If  bent  from  side  to  side  the  socket  will  become  en- 
larged and  the  shank  worn;  this  will  render  the  instrument  inac- 
curate. 


For  drawing  large  circles  the  lengthening  bar  shown  in 
When  using  the  lengthening  bar  the 


Fig.  IT  should  be  used. 


rr~bE=a 


e 


Fi<r.  20. 


Fig.  21. 


needle  point  should  be  steadied  with  one  hand  and  the  circle 
described  with  the  other. 

Dividers.  Dividers,  shown  in  Fig.  23,  are  made  similar  to  the 
compasses.  They  are  used  for  laying  off  distances  on  the  draw- 
ing, either  from  scales  or  from  other  parts  of  the  drawing.  They 

may  also  be  used  for  dividing  a line 
into  equal  parts.  When  dividing  a 
line  into  equal  parts  the  dividers 
should  be  turned  in  the  opposite  direc- 
tion each  time,  so  that  the  moving  point  passes  alternately  to 
the  right  and  to  the  left.  The  instrument  can  then  be  operated 
readily  with  one  hand.  The  points  of  the  dividers  should  be 
very  sharp  so  that  the  holes  made  in  the  paper  will  be  small. 
If  large  holes  are  made  in  the  paper,  and  the  distances  between 


EE 


19 


16 


MECHANICAL  DRAWING. 


the  points  are  not  exact,  accurate  spacing  cannot  be  done 
Sometimes  the  compasses  are  furnished  with  steel  divider  points 
in  addition  to  the  pen  and  pencil  points.  The  compasses  may 
then  be  used  either  as  dividers  or  as  compasses.  Many  drafts- 
men use  a needle  point  in  place  of  dividers  for  making  measure- 
ments from  a scale.  The  eye  end  of  a needle  is  first  broken  off 
and  the  needle  then  forced  into  a small  handle  made  of  a round 
piece  of  soft  pine.  This  instrument  is  very  convenient 
for  indicating  the  intersection  of  lines  and  marking  off 
distances. 

Bow  Pen  and  Bow  Pencil.  Ordinary  large  compasses 
are  too  heavy  to  use  in  making  small  circles,  fillets,  etc. 
The  leverage  of  the  long  leg  is  so  great  that  it  is  very 
difficult  to  draw  small  circles  accurately.  For  this  reason 
the  bow  compasses  shown  in  Figs.  24  and  25  should  be 
used  on  all  arcs  and  circles  having  a radius  of  less  than 
three-quarters  inch.  The  bow  compasses  are  also  con- 
venient for  duplicating  small  circles  such  as  those  which 
represent  boiler  tubes,  bolt  holes,  etc.,  since  there  is  no 
tendency  to  slip. 

The  needle  point  must  be  adjusted  to  the  same 
length  as  the  pen  or  pencil  point  if  very  small  circles  are 
to  be  drawn.  The  adjustment  for  altering  the  radius  of 
the  circle  can  be  made  by  turning  the  nut.  If  the  change 
in  radius  is  considerable  the  points  should  be  pressed  to- 
gether to  remove  the  pressure  from  the  nut  which  can 
then  be  turned  in  either  direction  with  but  little  wear  on 
the  threads. 

Fig.  26  shows  another  bow  instrument  which  is  frequently 
used  in  small  work  in  place  of  the  dividers.  It  has  the  advantage 
of  retaining  the  adjustment. 

Drawing  Pen.  For  drawing  straight  lines  and  curves  that 
are  not  arcs  of  circles,  the  line  pen  (sometimes  called  the  ruling 
pen)  is  used.  It  consists  of  two  blades  of  steel  fastened  to  a 
handle  as  shown  in  Fig.  27.  The  distance  between  the  pen  points 
can  be  adjusted  by  the  thumb  screw,  thus  regulating  the  width  of 
line  to  be  drawn.  The  blades  are  given  a slight  curvature  so  that 
there  will  be  a cavity  for  ink  when  the  points  are  close  together.. 


20 


MECHANICAL  DRAWING. 


17 


The  pen  may  be  filled  by  means  of  a common  steel  pen  or 
with  the  quill  which  is  provided  with  some  liquid  inks.  The  pen 
should  not  be  dipped  in  the  ink  because  it  will  then  be  necessary 
to  wipe  the  outside  of  the  blades  before  use.  The  ink  should 
fill  the  pen  to  a height  of  about  L or  | inch;  if  too  much  ink  is 
placed  in  the  pen  it  is  likely  to  drop  out  and  spoil  the  drawing. 
Upon  finishing  the  work  the  pen  should  be  carefully  wiped  with 


Fig.  24. 


Fig.  25. 


chamois  or  a soft  cloth,  because  most  liquid  inks  corrode  the  steel. 

In  using  the  pen,  care  should  be  taken  that  both  blades  bear 
equally  on  the  paper.  If  the  points  do  not  bear  equally  the  line 
will  be  ragged.  If  both  points  touch,  and  the  pen  is  in  good 
condition  the  line  will  be  smooth.  The  pen  is  usually  inclined 
slightly  in  the  direction  in  which  the  line  is  drawn.  The  pen 


Fig.  27. 


should  touch  the  triangle  or  T-square  which  serve  as  guides,  but 
it  should  not  be  pressed  against  them  because  the  lines  will  then 
be  uneven.  The  points  of  the  pen  should  be  close  to  the  edge  of 
the  triangle  or  T-square,  but  should  not  touch  it. 

To  Sharpen  the  Drawing  Pen.  After  the  pen  lias  been 
used  for  some  time  the  points  become  worn,  and  it  is  impossible 


21 


18 


MECHANICAL  DRAWING. 


to  make  smooth  lines.  This  is  especially  true  if  rough  paper  is 
used.  The  pen  can  be  put  in  proper  condition  by  sharpening  it. 
To  do  this  take  a small,  flat,  close-grained  oil-stone.  The  blades 
should  first  be  screwed  together,  and  the  points  of  the  pen  can  be 
given  the  proper  shape  by  drawing  the  pen  back  and  forth  over 
the  stone  changing  the  inclination  so  that  the  shape  of  the  ends 
will  be  parabolic.  This  process  dulls  the  points  but  gives  them 
the  proper  shape,  and  makes  them  of  the  same  length. 

To  sharpen  the  pen,  separate  the  points  slightly  and  rub  one 
of  them  on  the  oil-stone.  While  doing  this  keep  the  pen  at  an 
angle  of  from  10  to  15  degrees  with  the  face  of  the  stone,  and 
give  it  a slight  twisting  movement.  This  part  of  the  operation 
requires  great  care  as  the  shape  of  the  ends  must  not  be  altered. 
After  the  pen  point  has  become  fairly  sharp  the  other  point 
should  be  ground  in  the  same  manner.  All  the  grinding  should 
be  done  on  the  outside  of  the  blades.  The  burr  should  be 
removed  from  the  inside  of  the  blades  by  using  a piece  of  leather 
or  a piece  of  pine  wood. 

Ink  should  now  be  placed  between  the  blades  and  the  pen 
tried.  The  pen  should  make  a smooth  line  whether  fine  or 
heavy,  but  if  it  does  not  the  grinding  must  be  continued  and  the 
pen  tried  frequently. 

Ink.  India  ink  is  always  used  for  drawing  as  it  makes  a 
permanent  black  line.  It  may  be  purchased  in  solid  stick  form 
or  as  a liquid.  The  liquid  form  is  very  convenient  as  much  time 
is  saved,  and  all  the  lines  will  be  of  the  same  color ; the  acid  in 
the  ink,  however,  corrodes  steel  and  makes  it  necessary  to  keep 
the  pen  perfectly  clean. 

Some  draftsmen  prefer  to  use  the  India  ink  which  comes  in 
stick  form.  To  prepare  it  for  use,  a little  water  should  be  placed 
in  a saucer  and  one  end  of  the  stick  placed  in  it.  The  ink  is 
ground  by  giving  it  a twisting  movement.  When  the  water  has 
become  black  and  slightly  thickened,  it  should  be  tried.  A 
heavy  line  should  be  made  on  a sheet  of  paper  and  allowed  to 
dry.  If  the  line  has  a grayish  appearance,  more  grinding  is 
necessary.  After  the  ink  is  thick  enough  to  make  a good  black 
line,  the  grinding  should  cease,  because  very  thick  ink  will  not 
flow  freely  from  the  pen.  If,  however,  the  ink  has  become  too 


22 


MECHANICAL  DRAWING. 


19 


thick,  it  may  be  diluted  with  water.  After  using,  the  stick 
should  be  wiped  dry  to  prevent  crumbling.  It  is  well  to  grind 
the  ink  in  small  quantities  as  it  does  not  dissolve  readily  if  it  has 
once  become  dry.  If  the  ink  is  kept  covered  it  will  keep  for  two 
or  three  days. 

Scales.  Scales  are  used  for  obtaining  the  various  measure- 
ments on  drawings.  They  are  made  in  several  forms,  the  most 
convenient  being  the  flat  with  beveled  edges  and  the  triangular. 
The  scale  is  usually  a little  over  12  inches  long  and  is  graduated 
for  a distance  of  12  inches.  The  triangular  scale  shown  in  Fig. 
28  has  six  surfaces  for  graduations,  thus  allowing  many  gradua- 
tions on  the  same  scale. 

The  graduations  on  the  scales  are  arranged  so  that  the 
drawings  may  be  made  in  any  proportion  to  the  actual  size.  For 
mechanical  work,  the  common  divisions  are  multiples  of  two. 

A\\^\ 

Fig.  28. 

Thus  we  make  drawings  full  size,  half  size,  A,  ^ A-,  J^,  etc. 
If  a drawing  is  size,  8 inches  equals  1 foot,  hence  3 inches  is 
divided  into  12  equal  parts  and  each  division  represents  one  inch. 
If  the  smallest  division  04  a scale  represents  A-  inch,  the  scale  is 
said  to  read  to  -A  inch. 

Scales  are  often  divided  into  -A,  A_’  3V’  iV  e^c*’  ^or  archi‘ 
tects,  civil  engineers,  and  for  measuring  on  indicator  cards. 

The  scale  should  never  be  used  for  drawing  lines  in  place  of 
triangles  or  T-square. 

Protractor.  The  protractor  is  an  instrument  used  for  laying 
off  and  measuring  angles.  It  is  made  of  steel,  brass,  horn  and 
paper.  If  made  of  metal  the  central  portion  is  cut  out  as  shown 
in  Fig.  29,  so  that  the  draftsman  can  see  the  drawing.  The 
outer  edge  is  divided  into  degrees  and  tenths  of  degrees.  Some- 
times the  graduations  are  very  fine.  In  using  a protractor  a very 
sharp  hard  pencil  should  be  used  so  that  the  lines  will  be  fine 
and  accurate. 

The  protractor  should  be  placed  so  that  the  given  line  ( pro- 


23 


20 


MECHANICAL  DRAWING. 


duced  if  necessary ) coincides  with  the  two  O marks.  The 
center  of  the  circle  being  placed  at  the  point  through  which  the 
desired  line  is  to  be  drawn.  The  division  can  then  be  marked 
with  the  pencil  point  or  needle  point. 

Irregular  Curve.  One  of  the  conveniences  of  a draftsman’s 


outfit  is  the  French  or  irregular  curve.  It  is  made  of  wood, 
hard  rubber  or  celluloid,  the  last  named  material  being  the  best. 
It  is  made  in  various  shapes,  two  of  the  most  common  being 


shown  in  Fig.  30.  This  instrument  is  used  for  drawing  curves 
other  than  arcs  of  circles,  and  both  pencil  and  line  pen  can  be 
used. 

To  draw  the  curve,  a series  of  points  is  first  located  and 
then  the  curve  drawn  passing  through  them  by  using  the  part  of 
the  irregular  curve  that  passes  through  several  of  them.  The 


24 


MECHANICAL  DRAWING. 


21 


curve  is  shifted  for  this  work  from  one  position  to  another.  It 
frequently  facilitates  the  work  and  improves  its  appearance  to 
draw  a free  hand  pencil  curve  through  the  points  and  then  use  the 
irregular  curve,  taking  care  that  it  always  fits  at  least  three  points. 

In  inking  the  curve,  the  blades  of  the  pen  must  be  kept 


Fig.  31. 


tangent  to  the  curve,  thus  necessitating  a continual  change  of 
direction. 

Beam  Compasses.  The  ordinary  compasses  are  not  large 
enough  to  draw  circles  having  a diameter  greater  than  about  8 or 
10  inches.  A convenient  instrument  for  larger  circles  is  found 
in  the  beam  compasses  shown  in  Fig.  31.  The  two  parts  called 
channels  carrying  the  pen  or  pencil  and  the  needle  point  are 
clamped  to  a wooden  beam  ; the  distance  between  them  being 
equal  to  the  radius  of  the  circle.  Accurate  adjustment  is  obtained 
by  means  of  a thumb  nut  underneath  one  of  the  channel  pieces. 

LETTERING. 

No  mechanical  drawing  is  finished  unless  all  headings,  titles 
and  dimensions  are  lettered  in  plain,  neat  type.  Many  drawings 
are  accurate,  well-planned  and  finely  executed  but  do  not  present 
a good  appearance  because  the  draftsman  did  not  think  it  worth 
while  to  letter  well.  Lettering  requires  time  and  patience; 
and  if  one  wishes  to  letter  rapidly  and  well  he  must  practice. 

Usually  a beginner  cannot  letter  well,  and  in  order  to  pro- 
duce a satisfactory  result,  considerable  practice  is  necessary.  Many 


25 


MECHANICAL  DRAWING 


think  it  a good  plan  to  practice  lettering  before  commencing  a 
drawing.  A good  writer  does  not  always  letter  well ; a poor 
writer  need  not  be  discouraged  and  think  he  can  never  learn  to 
make  a neatly  lettered  drawing. 

In  making  large  letters  for  titles  and  headings  it  is  often 
necessary  to  use  drawing  instruments  and  mechanical  aids.  The 
small  letters,  such  as  those  used  for  dimensions,  names  of  materials, 
dates,  etc.,  should  be  made  free  hand. 

There  are  many  styles  of  letters  used  by  draftsmen.  For 
titles,  large  Roman  capitals  are  frequently  used,  although  Gothic 
and  block  letters  also  look  well  and  are  much  easier  to  make. 

ABCDEFGHIJ 

KLMNOPOR 

STUVWXYZ 

1234567890 

Fig.  32. 

Almost  any  neat  letter  free  from  ornamentation  is  acceptable  in  the 
regular  practice  of  drafting.  Fig.  32  shows  the  alphabet  oi 
vertical  Gothic  capitals.  These  letters  are  neat,  plain  and  easily 
made.  The  inclined  or  italicized  Gothic  type  is  shown  in  Fig.  33. 
This  style  is  also  easy  to  construct,  and  possesses  the  advantage 
that  a slight  difference  in  inclination  is  not  apparent.  If  the  ver- 
tical lines  of  the  vertical  letters  incline  slightly  the  inaccuracy  is 
very  noticeable. 

The  curves  of  the  inclined  Gothic  letters  such  as  those  in  the 
B , 6Y,  6r,  </,  etc.,  are  somewhat  difficult  to  make  free  hand, 
especially  if  the  letters  are  about  one-half  inch  high.  In  the 
alphabet  shown  in  Fig.  34,  the  letters  are  made  almost  wholly  of 


26 


MECHANICAL  DRAWING. 


23 


straight  lines,  the  corners  only  being  curved.  These  letters  are 
very  easy  to  make  and  are  clear  cut. 

The  first  few  plates  of  this  work  will  require  no  titles ; the 
only  lettering  being  the  student’s  name,  together  with  the  date 
and  plate  number.  Later,  the  student  will  take  up  the  subject  of 


KL  MNORQH 
S TU  VWX  YZ 

Fig.  33. 

lettering  again  in  order  to  letter  titles  and  headings  for  drawings 
showing  the  details  of  machines.  For  the  present,  however,  in- 
clined Gothic  capitals  will  be  used. 

To  make  the  inclined  Gothic  letters,  first  draw  two  parallel 
lines  having  the  distance  between  them  equal  to  the  desired  height 
of  the  letters.  If  two  sizes  of  letters  are  to  be  used,  the  smaller 
should  be  about  two-thirds  as  high  as  the  larger.  For  the  letters 

,4 BCDETGH/JKLM 
NOPQFt  S TU  VWX  YZ 
193-4587890 

Fig.  34. 

to  be  used  on  the  first  plates,  draw  two  parallel  lines  ^ inch  apart. 
This  is  the  height  for  the  letters  of  the  date,  name,  also  the  plate 
number,  and  should  be  used  on  all  plates  throughout  this  work, 
unless  other  directions  are  given. 

In  constructing  the  letters,  they  should  extend  fully  to  these 
lines,  both  at  the  top  and  bottom.  They  should  not  fall  short  of 


27 


24 


MECHANICAL  DRAWING. 


the  guide  lines  nor  extend  beyond  them.  As  these  letters  are- 
inclined  they  will  look  better  if  the  inclination  is  the  same  for  all. 
As  an  aid  to  the  beginner,  he  can  draw  light  pencil  lines,  about  | 
inch  apart,  forming  the  proper  angle  with  the  parallel  lines  already 
drawn.  The  inclination  is  often  made  about  70  degrees ; but  as  a 
60-degree  triangle  is  at  hand,  it  may  be  used.  To  draw  these 
lines  place  the  60-degree  triangle  on  the  T-square  as  shown  in 
Fig.  36.  In  making  these  letters  the  60-degree  lines  will  be 
found  a great  aid  as  a large  proportion  of  the  back  or  side  lines 
have  this  inclination. 

Capital  letters  such  as  E,  F , P,  T,  Z , etc.,  should  have  the 
top  lines  coincide  with  the  upper  horizontal  guide  line.  The 
bottom  lines  of  such  letters  as  Z),  P,  P,  Z , etc.,  should  coincide 
with  the  lower  horizontal  guide  line.  If  these  lines  do  not  coin- 
cide with  the  guide  lines  the  words  will  look  uneven.  Letters, 
of  which  (7,  6r,  0,  and  Q,  are  types,  can  be  formed  of  curved  lines 
or  of  straight  lines.  If  made  of  curved  lines,  they  should  have  a 
little  greater  height  than  the  guide  lines  to  prevent  their  appear- 
ing smaller  than  the  other  letters.  In  this  work  they  can  be 
made  of  straight  lines  with  rounded  corners  as  they  are  easily 
constructed  and  the  student  can  make  all  letters  of  the  same 
height. 

To  construct  the  letter  A , draw  a line  at  an  angle  of  60 
degrees  to  the  horizontal  and  use  it  as  a center  line.  Then  from 
the  intersection  of  this  line  and  the  upper  horizontal  line  drop 
a vertical  line  to  the  lower  guide  line.  Draw  another  line  from 
the  vertex  meeting  the  lower  guide  line  at  the  same  distance  from 
the  center  line.  The  cross  line  of  the  A should  be  a little  below 
the  center.  The  Pis  an  inverted  A without  the  cross  line.  For 
the  letter  AT,  the  side  lines  should  be  parallel  and  about  the  same 
distance  apart  as  are  the  horizontal  lines.  The  side  lines  of  the 
W are  not  parallel  but  are  farther  apart  at  the  top.  The  J is  not 
quite  as  wide  as  such  letters  as  H ’ E , 2V,  P,  etc.  To  make  a Y. 
draw  the  center  line  60  degrees  to  the  horizontal ; the  diverg- 
ing lines  are  similar  to  those  of  the  V but  are  shorter  and  form  a 
larger  angle.  The  diverging  lines  should  meet  the  center  line  a 
little  below  the  middle. 

The  lower-case  letters  are  shown  in  Fig.  35.  In  such  letters 


28 


MECHANICAL  DRAWING. 


25 


as  n,  r,  etc.,  make  the  corners  sharp  and  not  rounding.  The 
letters  a,  b,  c,  e , g , 0,  g,  should  be  full  and  roundifig.  The 
figures  (see  Fig.  32)  are  made  as  in  writing  — except  the  6,8 
and  9. 

The  Roman  numerals  are  made  of  straight  lines  as  they 
are  largely  made  up  of  1 V and  X. 

At  first  the  copy  should  be  followed  closely  and  the  letters 
drawn  in  pencil.  For  a time,  the  inclined  guide  lines  may  be  used. 

abcdefgh/jk/mn 
opqrs  t u vwxjsz 

Fig.  35. 

but  after  the  proper  inclination  becomes  firmly  fixed  in  mind 
they  should  be  abandoned.  The  horizontal  lines  are  used  at  all 
times  by  most  draftsmen.  After  the  student  has  had  consider- 
able practice,  he  can  construct  the  letters  in  ink  without  first  using 
the  pencil.  Later  in  the  work,  when  the  student  has  become  pro- 
ficient in  the  simple  inclined  Gothic  capitals,  the  vertical,  block 
and  Roman  alphabets  should  be  studied. 

PLATES, 

To  lay  out  a sheet  of  paper  for  the  plates  of  this  work,  the 
sheet,  A B G F,  (Fig.  36)  is  placed  on  the  drawing  board  2 or  3 
inches  from  the  left-hand  edge  which  is  called  the  working  edge . 
If  placed  near  the  left-hand  edge,  the  T-square  and  triangles  can 
be  used  with  greater  firmness  and  the  horizontal  lines  drawn  with 
the  T-square  will  be  more  accurate.  In  placing  the  paper  on  the 
board,  always  true  it  up  according  to  the  long  edge  of  the  sheet. 
First  fasten  the  paper  to  the  board  with  thumb  tacks,  using  at 
least  4 — one  at  each  corner.  If  the  paper  has  a tendency  to  curl 
it  is  better  to  use  6 or  8 tacks,  placing  them  as  shown  in  Fig.  36. 
Thumb  tacks  are  commonly  used;  but  many  draftsmen  prefer 
one-ounce  tacks  as  they  offer  less  obstruction  to  the  T-square  and 
triangles. 

After  the  paper  is  fastened  in  position,  find  the  center  of  the 


/ 


29 


26 


MECHANICAL  DRAWING. 


Fig.  36. 


MECHANICAL  DRAWING. 


27 


sheet  by  placing  the  T-square  so  that  its  upper  edge  coincides  with 
the  diagonal  corners  A and  G and  then  with  the  corners  F and 
B,  drawing  short  pencil  lines  intersecting  at  C.  Now  place  the 
T-square  so  that  its  upper  edge  coincides  with 'the  point  C and 
draw  the  dot  and  dash  line  D E.  With  the  T-square  and  one 
of  the  triangles  (shown  dotted)  in  the  position  shown  in  Fig.  36, 
draw  the  dot  and  dash  line  H C K.  In  case  the  drawing  board 
is  large  enough,  the  line  C H can  be  drawn  by  moving  the  T- 
square  until  it  is  entirely  off  the  drawing.  If  the  board  is  small, 
produce  (extend)  the  line  K C to  H by  means  of  the  T-square 
or  edge  of  a triangle.  In  this  work  always  move  the  pencil  from 
the  left  to  the  right  or  from  the  bottom  upward;  never  (except 
for  some  particular  purpose)  in  the  opposite  direction. 

After  the  center  lines  are  drawn  measure  off  5 inches  above 
and  below  the  point  C on  the  line  II  C K.  These  points  L 
and  M may  be  indicated  by  a light  pencil  mark  or  by  a slight 
puncture  of  one  of  the  points  of  the  dividers.  Now  place  the  T- 
square  against  the  left-hand  edge  of  the  board  and  draw  horizontal 
pencil  lines  through  L and  M. 

Measure  off  7 inches  to  the  left  and  right  of  C on  the  center 
line  I)  C E and  draw  pencil  lines  through  these  points  (N  and 
P)  perpendicular  to  D E.  We  now  have  a rectangle  10  inches 
by  14  inches,  in  which  all  the  exercises  and  figures  are  to  be 
drawn.  The  lettering  of  the  student’s  name  and  address,  date, 
and  plate  number  are  to  be  placed  outside  of  this  rectangle  in  the 
i-inch  margin.  In  all  cases  lay  out  the  plates  in  this  manner  and 
keep  the  center  lines  D E and  K H as  a basis  for  the  various 
figures.  The  bor’d er  line  is  to  be  inked  with  a heavy  line  when 
the  drawing  is  inked. 

Pencilling.  Inlaying  out  plates,  all  work  is  first  done  in  pen- 
cil and  afterward  inked  or  traced  on  tracing  cloth.  The  first  few 
plates  of  this  course  are  to  be  done  in  pencil  and  then  inked  ; later 
the  subject  of  tracing  and  the  process  of  making  blue  prints  will 
be  taken  up.  Every  beginner  should  practice  with  his  instruments 
until  he  can  use  them  with  accuracy  and  skill,  and  until  he  under- 
stands thoroughly  what  instrument  should  be  used  for  making  a 
given  line.  To  aid  the  beginner  in  this  work,  the  first  three  plates 
of  this  course  are  designed  to  give  the  student  practice ; they  do 


31 


28 


MECHANICAL  DRAWING. 


not  involve  any  problems  and  none  of  the  work  is  difficult.  The 
student  is  strongly  advised  to  draw  these  plates  two  or  three 
times  before  making  the  one  to  be  sent  to  us  for  correction.  Dili- 
gent practice  is  necessary  at  first;  especially  on  PLATE  I as  it 
involves  an  exercise  in  lettering. 

PLATE  I. 

Pencilling.  To  draw  PLATE  1 , take  a sheet  of  drawing 
paper  at  least  11  inches  by  15  inches  and  fasten  it  to  the  drawing 
board  as  already  explained.  Find  the  center  of  the  sheet  and  draw 
fine  pencil  lines  to  represent  the  lines  D E and  H K of  Fig.  36. 
Also  draw  the  border  lines  L,  M,  N and  P. 

Now  measure  |-  inch  above  and  below  the  horizontal  center  line 
and,  with  the  T-square,  draw  lines  through  these  points.  These 
lines  will  form  the  lower  lines  D C of  Figs.  1 and  2 and  the  top  lines 
A B of  Figs.  3 and  J^.  Measure  |-  inch  to  the  right  and  left  of  the 
vertical  center  line ; and  through  these  points,  draw  lines  parallel 
to  the  center  line.  These  lines  should  be  drawn  by  placing  the 
triangle  on  the  T-square  as  shown  in  Fig.  36.  The  lines  thus 
drawn,  form  the  sides  B C of  Figs.  1 and  3 and  the  sides  A D of 
Figs.  2 and  Jj,.  Next  draw  the  line  A B A B with  the  T-square, 
4|  inches  above  the  horizontal  center  line.  This  line  forms  the 
top  lines  of  Figs.  1 and  2.  Now  draw  the  line  D C D C 4|  inches 
below  the  horizontal  center  line.  The  rectangles  of  the  four 
figures  are  completed  by  drawing  vertical  lines  6|  inches  from  the 
vertical  center  line.  We  now  have  four  rectangles  each  6J  inches 
long  and  41  inches  wide. 

Fig.  1 is  an  exercise  with  the  line  pen  and  T-square.  Divide 
the  line  A D into  divisions  each  I inch  long,  making  a fine  pencil 
point  or  slight  puncture  at  each  division  such  as  E,  F,  G,  H,  I,  etc. 
Now  place  the  T-square  with  the  head  at  the  left-hand  edge  of  the 
drawing  board  and  through  these  points  draw  light  pencil  lines 
extending  to  the  line  B C.  In  drawing  these  lines  be  careful  to 
have  the  pencil  point  pass  exactly  through  the  division  marks  so 
that  the  lines  will  be  the  same  distance  apart.  Start  each  line  in 
the  line  A D and  do  not  fall  short  of  the  line  B C or  run  over  it. 
Accuracy  and  neatness  in  pencilling  insure  an  accurate  drawing. 
Some  beginners  think  that  they  can  correct  inaccuracies  while 


32 


PLATE 


EANUARR  /.  / 9 O /.  HERBERT  ERA  A/EL  ER  CH/CAGO,  /LL 


MECHANICAL  DRAWING.  29 


inking;  but  experience  soon  teaches  them  that  they  cannot  do  so. 

Fig . 2 is  an  exercise  with  the  line  pen,  T-square  and  triangle. 
First  divide  the  lower  line  1)  C of  the  rectangle  into  divisions  each 
| inch  long  and  mark  the  points  E,  F,  G,  H,  I,  J,  K,  etc.,  as  in 
Fig . 1.  Place  the  T-square  with  the  head  at  the  left-hand  edge  of 
the  drawing  board  and  the  upper  edge  in  about  the  position  shown 
in  Fig.  36.  Place  either  triangle  with  one  edge  on  the  upper  edge 
of  the  T-square  and  the  90-degree  angle  at  the  left.  Now  draw 
fine  pencil  lines  from  the  line  D C to  the  line  A B passing  through 
the  points  E,  F,  G,  H,  I,  J,  K,  etc.  To  do  this  keep  the  T-square 


E 

/ /•  / / A RJN  & 

T7-TF  STTB77~ 

rinhA/  ~ 

AK/tf'.AJ 

-rx'F'nt  r~ 

7JTFF/n~ 

Frnt  7 07&71 

by  jur-QCl/CEi 

AF/'?/?F  ~ 

p '■  a beds 

Z23-4 

7 77  777  TV 

Z 

Fig.  37. 


rigid  and  slide  the  triangle  toward  the  right,  being  careful  to  have 
the  edore  coincide  with  the  division  marks  in  succession. 

Fig.  Jis  an  exercise  with  the  line  pen,  T-square  and  45-degree 
triangle.  First  lay  off  the  distances  A E,  E F,  F G,  G H,  H I,  I J, 
J K,  etc.,  each  1 inch  long.  Then  lay  off  the  distances  B L,  L M, 
M N,  N O,  O P,  P Q,  Q R,  etc.,  also  i inch  long.  Place  the  T- 
square  so  that  the  upper  edge  will  be  below  the  line  I)  C of  Fig.  3. 
With  the  45-degree  triangle  draw  lines  from  AD  and  DC  to 
the  points  E,  F,  G,  H,  I,  J,  K,  etc.,  as  far  as  the  point  B.  Now 
draw  lines  from  D C to  the  points  L,  M,  N,  (),  P,  Q,  R,  etc.,  as 


35 


80 


MECHANICAL  DRAWING. 


far  as  the  point  C.  In  drawing  these  lines  move  the  pencil  away 
from  the  body,  that  is,  from  A D to  A B and  from  D C to  B C. 

Fig.  Jj>  is  an  exercise  in  free-hand  lettering.  The  finished 
exercise,  with  all  guide  lines  erased,  should  have  the  appearance 
shown  in  Fig . ^ of  PLATE  I.  The  guide  lines  are  drawn  as  shown 
in  Fig.  37.  First  draw  the  center  line  E F and  light  pencil  lines 
Y Z and  T X,  | inch  from  the  border  lines.  Now,  with  the  T- 
square,  draw  the  line  G,  i inch  from  the  top  line  and  the  line  H, 
^ inch  below  G.  The  word  “ LETTERING-  ” is  to  be  placed 
between  these  two  lines.  Draw  the  line  I,  ^ inch  below  H. 
The  lines  I,  J,  etc.,  to  K are  all  ^ inch  apart. 

We  now  practice  the  lower-case  letters.  Draw  the  line  L, 
inch  below  K and  a light  line  l inch  above  L to  limit  the 
height  of  the  small  letters.  The  space  between  L and  M is 
inch.  The  lines  M and  N are  drawn  in  the  same  manner  as  K and 
L.  The  space  between  N and  O should  be  l inch.  The  line  P is 
drawn  ^ inch  below  O.  Q is  also  A inch  below  P.  The  lines 
Q and  R are  drawn  inch  apart  as  are  M and  N.  The  remainder 
of  the  lines  S,  U,  V and  W are  drawn  g52-  inch  apart. 

The  center  line  is  a great  aid  in  centering  the  word 
“ LETTERING^”  the  alphabets,  numerals,  etc.  The  words 
UTIIE”  and  “ Proficiency  ” should  be  indented  about  -| 
inch  as  they  are  the  first  words  of  paragraphs.  To  draw  the 
guide  lines,  mark  off  distances  of  1 inch  on  any  line  such  as  J and 
with  the  60-degree  triangle  draw  light  pencil  lines  cutting  the 
parallel  lines.  The  letters  should  be  sketched  in  pencil,  the  ordin- 
ary letters  such  as  E,  F,  H,  N,  R,  etc.  being  made  of  a width 
equal  to  about  | the  height.  Letters  like  A,  M and  W are  wider. 
The  space  between  the  letters  depends  upon  the  draftsman’s 
taste  but  the  beginner  should  remember  that  letters  next  to  an 
A or  an  L should  be  placed  near  them  and  that  greater  space 
should  be  left  on  each  side  of  an  I or  between  letters  whose  sides  are 
parallel;  for  instance  there  should  be  more  space  between  an  N and 
E than  between  an  E and  FI.  On  account  of  the  space  above  the 
lower  line  of  the  L,  a letter  following  an  L should  be  close  to  it 
If  a T follows  a T or  the  letter  L follows  an  L they  should  be 
placed  near  together.  In  all  lettering  the  letters  should  be  placed 
so  that  the  general  effect  is  pleasing.  After  the  four  figures  are 


86 


MECHANICAL  DRAWING. 


31 


completed,  the  lettering  for  name,  address  and  date  should  be 
pencilled.  With  the  T-square  draw  a pencil  line  inch  above 
the  top  border  line  at  the  right-hand  end.  This  line  should  be 
about  3 inches  long.  At  a distance  of  inch  above  this  line  draw 
another. line  of  about  the  same  length.  These  are  the  guide  lines 
for  the  word  PLATE  I.  The  letters  should  be  pencilled  free 
hand  and  the  student  may  use  the  60-degree  guide  lines  if  he 
desires. 

The  guide  lines  of  the  date,  name  and  address  are  similarly 
drawn  in  the  lower  margin.  The  date  of  completing  the  drawing 
should  be  placed  under  Fig.  3 and  the  name  and  address  at  the 
right  under  Fig.  4*  The  street  address  is  unnecessary.  It  is  a 
good  plan  to  draw  lines  -fa  inch  apart  on  a separate  sheet  of  paper 
and  pencil  the  letters  in  order  to  know  just  how  much  space  each 
word  will  require.  The  insertion  of  the  words  “ Fig.  1 ,”  “ Fig. 
2”  etc.,  is  optional  with  the  student.  He  may  leave  them  out  if  he 
desires  ; but  we  would  advise  him  to  do  this  extra  lettering  for  the 
practice  and  for  convenience  in  reference.  First  draw  with  the 
T-square  two  parallel  line  ^ inch  apart  under  each  exercise ; the 
lower  line  being  Ag  inch  above  the  horizontal  center  line  or  above 
the  lower  border  line. 

Inking.  After  all  of  the  pencilling  of  PLATE  I has  been 
completed  the  exercises  should  be  inked.  The  pen  should  first  be 
examined  to  make  sure  that  the  nibs  are  clean,  of  the  same  length 
and  come  together  evenly.  To  fill  the  pen  with  ink  use  an  ordi- 
nary steel  pen  or  the  quill  in  the  bottle,  if  Higgin’s  Ink  is  used. 
Dip  the  quill  or  pen  into  the  bottle  and  then  inside  between  the 
nibs  of  the  line  pen.  The  ink  will  readily  flow  from  the  quill  into 
the  space  between  the  nibs  as  soon  as  it  is  brought  in  contact.  Do 
not  fill  the  pen  too  full,  if  the  ink  fills  about  ^ the  distance  to  the 
adjusting  screw  it  usually  will  be  sufficient.  If  the  filling  has  been 
carefully  done  it  will  not  be  necessary  to  wipe  the  outsides  of  the 
blades.  However,  any  ink  on  the  outside  should  be  wiped  off 
with  a soft  cloth  or  a piece  of  chamois. 

The  pen  should  now  be  tried  on  a separate  piece  of  paper  in 
order  that  the  width  of  the  line  may  be  adjusted.  In  the  first 
work  where  no  shading  is  done,  a firm  distinct  line  should  be  used. 
The  beginner  should  avoid  the  extremes : a very  light  line  makes 


37 


32 


MECHANICAL  DRAWING. 


the  drawing  have  a weak,  indistinct  appearance,  and  very  heavy 
lines  detract  from  the  artistic  appearance  and  make  the  drawing 
appear  heavy. 

In  case  the  ink  does  not  flow  freely,  wet  the  finger  and  touch 
it  to  the  end  of  the  pen.  If  it  then  fails  to  flow,  draw  a slip  of 
thin  paper  between  the  nibs  (thus  removing  the  dried  ink)  or 
clean  thoroughly  and  fill.  Never  lay  the  pen  aside  without 
cleaning. 

In  ruling  with  the  line  pen  it  should  be  held  firmly  in  the 
right  hand  almost  perpendicular  to  the  paper.  If  grasped  too 
firmly  the  width  of  the  line  may  be  varied  and  the  draftsman 
soon  becomes  fatigued.  The  pen  is  usually  held  so  that  the 
adjusting  screw  is  away  from  the  T-square,  triangles,  etc.  Many 
draftsmen  incline  the  pen  slightly  in  the  direction  in  which  it  is 
moving. 

To  ink  Fig.  i,  place  the  T-square  with  the  head  at  the  work- 
ing edge  as  in  pencilling.  First  ink  all  of  the  horizontal  lines 
moving  the  T-square  from  A to  D.  In  drawing  these  lines  con- 
siderable care  is  necessary ; both  nibs  should  touch  the  paper  and 
the  pressure  should  be  uniform.  Have  sufficient  ink  in  the  pen 
to  finish  the  line  as  it  is  difficult  for  a beginner  to  stop  in  the 
middle  of  the  line  and  after  refilling  the  pen  make  a smooth  con- 
tinuous line.  While  inking  the  lines  A,  E,  F,  G,  H,  I,  etc.,  greater 
care  should  be  taken  in  starting  and  stopping  than  while  pencib 
Hng.  Each  line  should  start  exactly  in  the  pencil  line  A D and 
stop  in  the  line  B C.  The  lines  A D and  B C are  inked,  using 
the  triangle  and  T-square. 

Fig.  2 is  inked  in  the  same  manner  as  it  was  pencilled ; the 
lines  being  drawn,  sliding  the  triangle  along  the  T-square  in  the 
successive  positions. 

In  inking  Fig.  3,  the  same  care  is  necessary  as  with  the  pre- 
ceding, and  after  the  oblique  lines  are  inked  the  border  lines  are 
finished.  In  Fig.  Jj.  the  border  lines  should  be  inked  in  first 
and  then  the  border  lines  of  the  plate.  The  border  lines  should 
be  quite  heavy  as  they  give  the  plate  a better  appearance.  The 
intersections  should  be  accurate,  as  any  running  over  necessitates 
erasing. 

The  line  pen  may  now  be  cleaned  and  laid  aside.  It  can  be 


38 


RLATE 


MECHANICAL  DRAWING. 


33 


cleaned  by  drawing  a strip  of  blotting  paper  between  the  nibs  or 
by  means  of  a piece  of  cloth  or  chamois.  The  lettering  should  be 
done  free-hand  using  a steel  pen.  If  the  pen  is  very  fine,  accu- 
rate work  may  be  done  but  the  pen  is  likely  to  catch  in  the  paper, 
especially  if  the  paper,  is  rough.  A coarser  pen  will  make  broader 
lines  but  is  on  the  whole  preferable.  Gillott’s  404  is  as  fine  a 
pen  as  should  be  used.  After  inking  Fig.  4,  the  plate  number, 
date  and  name  should  be  inked,  also  free-hand.  After  ink- 
ing the  words  “ Fig.  1 ,”  “ Fig.  2”  etc.,  all  pencil  lines  should 
be  erased.  In  the  finished  drawing  there  should  be  no  center 
lines,  construction  lines  or  letters  other  than  those  in  the 
name,  date,  etc. 

The  sheet  should  be  cut  to  a size  of  n inches  by  15  inches, 

the  dash  line  outside  the  border  line  of  PLATE  /indicating  the 
edge. 

PLATE  II. 

Pencilling.  The  drawing  paper  used  for  PLATE  //should 
be  laid  out  as  described  with  PLATE  1,  that  is,  the  border  lines, 
center  line  and  rectangles  for  Figs.  1 and  2.  To  lay  out  Figs.  3, 
Ij,  and  5 proceed  as  follows  : Draw  a line  with  the  T-square 

parallel  to  the  horizontal  center  line  and  | inch  below  it.  Also 
draw  another  similar  line  4|  below  the  centerline.  The  two  lines 
will  form  the  top  and  bottom  of  Figs.  3,  ^ and  5.  Now  measure 
off  2L  inches  on  either  side  of  the  center  on  the  horizontal  center 
line  and  call  the  points  Y and  Z.  On  either  side  of  Y and  Z and 
at  a distance  of  L inch  draw  vertical  parallel  lines.  Now  draw  a 
vertical  line  A D,  4L  inches  from  the  line  Y and  a vertical  line 
B C 4|  inches  from  the  line  Z.  We  now  have  three  rectangles 
each  4 inches  broad  and  4|  inches  high.  Figs.  1 and  2 are  pen- 
reined  in  exactly  the  same  way  as  was  Fig.  1 of  PLATE  /,  that 
is,  horizontal  lines  are  drawn  i inch  apart. 

Fig.  3 is  an  exercise  to  show  the  use  of  a 60-degree  triangle 
with  a T-square.  Lay  off  the  distances  A E,  E F,  F G,  G H,  etc. 
to  B each  L inch.  With  the  60  degree  triangle  resting  on  the 
upper  edge  of  the  T-square,  draw  lines  through  these  points,  E,  F, 
G,  H,  I,  J,  etc.,  forming  an  angle  of  30  degrees  with  the  hori- 
zontal. The  last  line  drawn  willfbe  A L.  In  drawing  these  lines 
move  the  pencil  from  A B to  B C.  Now  find  the  distance 


41 


34 


MECHANICAL  DRAWING. 


between  the  lines  on  the  vertical  B L and  mark  off  these  distances 
on  the  line  B C commencing  at  L.  Continue  the  lines  from  A L 
to  N C.  Commencing  at  N mark  off  distances  on  A D equal 
to  those  on  B C and  finish  drawing  the  oblique  lines. 

Fig.  £ is  an  exercise  for  intersection.  Lay  off  distances  of 
-i  inch  on  A B and  A D.  With  the  T-square  draw  fine  pencil 
lines  through  the  points  E,  F,  G,  H,  I,  etc.,  and  with  the  T-square 
and  triangle  draw  vertical  lines  through  the  points  L,  M,  N,  O,  P, 
etc.  In  drawing  this  figure  draw  every  line  exactly  through  the 
points  indicated  as  the  symmetrical  appearance  of  the  small 
squares  can  be  attained  only  by  accurate  pencilling. 

The  oblique  lines  in  Fig.  5 form  an  angle  of  60  degrees  with 
the  horizontal.  As  in  Figs.  3 and  Jf  mark  off  the  line  A B in 
divisions  of  1 inch  and  draw  with  the  T-square  and  60-degree 
triangle  the  oblique  lines  through  these  points  of  division  moving 
the  pencil  from  A B to  B C.  The  last  line  thus  drawn  will  be 
A L.  Now  mark  off  distances  of  ^ inch  on  C D beginning  at  L. 
The  lines  may  now  be  finished. 

Inking.  Fig.  1 is  designed  to  give  the  beginner  practice  in 
drawing  lines  of  varying  widths.  The  line  E is  first  drawii.  This 
line  should  be  rather  fine  but  should  be  clear  and  distinct.  The 
line  F should  be  a little  wider  than  E ; the  greater  width  being 
obtained  by  turning  the  adjusting  screw  from  one-quarter  to  one- 
half  a turn.  The  lines  G,  H,  I,  etc.,  are  drawn ; each  successive 
line  having  greater  width.  M and  N should  be  the  same  and 
quite  heavy.  From  N to  D the  lines  should  decrease  in  width. 
To  complete  the  inking  of  Fig.  1 , draw  the  border  lines.  These 
lines  should  have  about  the  same  width  as  those  in  PLATE  I. 

In  Fig.  2 the  first  four  lines  should  be  dotted.  The  dots  should 
be  uniform  in  length  (about  inch)  and  the  spaces  also  uniform 
(about  -Jg-  inch).  The  next  four  lines  are  dash  lines  similar  to 
those  used  for  dimensions.  These  lines  should  be  drawn  with 
dashes  about  £ inch  long  and  the  lines  should  be  fine,  yet  distinct. 

The  following  four  lines  are  called  dot  and  dash  lines.  The 
dashes  are  about  | inch  long  and  a dot  between  as  shown.  In 
the  regular  practice  of  drafting  the  length  of  the  dashes  depends 
upon  the  size  of  the  drawing  — 1 inch  to  1 inch  being  common. 
The  last  lour  lines  are  similar,  two  dots  being  used  between  the 


4 2 


MECHANICAL  DRAWING. 


35 


dashes.  After  completing  the  dot  and  dash  lines,  draw  the  border 
lines  of  the  rectangle  as  before. 

In  inking  Fig.  3,  the  pencil  lines  are  followed.  Great  care 
should  be  exercised  in  starting  and  stopping.  The  lines  should 
begin  in  the  border  lines  and  the  end  should  not  run  over. 

The  lines  of  Fig.  If  must  be  drawn  carefully,  as  there  are  so 
many  intersections.  The  lines  in  this  figure  should  be  lighter  than 
the  border  lines.  If  every  line  does  not  coincide  with  the  points 
of  division  L,  M,  N,  O,  P,  etc.,  some  will  appear  farther  apart 
than  others. 

Fig.  5 is  similar  to  Fig.  3 , the  only  difference  being  in  the 
angle  which  the  oblique  lines  make  with  the  horizontal. 

After  completing  the  five  figures  draw  the  border  lines  of  the 
plate  and  then  letter  the  plate  number,  date  and  name,  and  the 
figure  numbers,  as  in  PLATE  I.  The  plate  should  then  be 
cut  to  the  required  size,  u inches  by  15  inches. 

PLATE  III. 

Pencilling.  The  horizontal  and  vertical  center  lines  and  the 
border  lines  for  PLATE  ILL  are  laid  out  in  the  same  manner  as 
were  those  of  PLATE  II.  To  draw  the  squares  for  the  six  figures, 
proceed  as  follows  : 

Measure  off  two  inches  on  either  side  of  the  vertical  center 
line  and  draw  light  pencil  lines  through  these  points  parallel  to 
the  vertical  center  line.  These  lines  will  form  the  sides  A D and 
B C of  Figs.  2 and  5.  Parallel  to  these  lines  and  at  a distance  of 
I inch  draw  similar  lines  to  form  the  sides  B C of  Figs.  1 and  If 
and  A D of  Figs.  3 and  6.  The  vertical  sides  A D of  Figs.  1 and 
If  and  B C of  Figs.  3 and  6 are  formed  by  drawing  lines  perpen- 
dicular to  the  horizontal  center  line  at  a distance  of  6^  inches  from 
the  center. 

The  horizontal  sides  D C of  Figs.  1 , 2 and  3 are  drawn  with 
the  T-square  I inch  above  the  horizontal  center  line.  To  draw  the 
top  lines  of  these  figures,  draw  (with  the  T-square)  a line  4J  inches 
above  the  horizontal  center  line.  The  top  lines  of  Figs.  If,  5 and 
6 are  drawn  1 inch  below  the  horizontal  center  line.  The  squares 
are  completed  by  drawing  the  lower  lines  D C,  41  inches  below 
the  horizontal  center  line.  The  figures  of  PLATES  I and  II 


43 


36 


MECHANICAL  DRAWING. 


were  constructed  in  rectangles  ; the  exercises  of  PL  A TE  III  are, 
however,  drawn  in  squares,  having  the  sides  4 inches  long. 

In  drawing  Fig.  1,  first  divide  A D and  A B (or  DC)  into 
4 equal  parts.  As  these  lines  are  four  inches  long,  each  length  will 
be  1 inch.  Now  draw  horizontal  .lines  through  E,  F and  G and 
vertical  lines  through  L,  M and  N.  These  lines  are  shown  dotted 
in  Fig.  1 . Connect  A and  B with  the  intersection  of  lines  E 
and  M,  and  A and  D with  the  intersection  of  lines  F and  L. 
Similarly  draw  D J,  J C,  I B and  I C.  Also  connect  the  points  P, 
O,  I and  J forming  a square.  The  four  diamond  shaped  areas 
are  formed  by  drawing  lines  from  the  middle  points  of  A D,  A B, 
B C and  D C to  the  middle  points  of  lines  A P,  A O,  O B,  I B 
etc.,  as  shown  in  Fig.  1. 

Fig . 2 is  an  exercise  of  straight  lines.  Divide  A D and  A B 
into  four  equal  parts  and  draw  horizontal  and  vertical  lines  as  in 
Fig . i.  Now  divide  these  dimensions,  A L,  M N,  etc.  and  E F, 
G B etc.  into  four  equal  parts  ( each  ^ inch  ) . Draw  light 
pencil  lines  with  the  T-square  and  triangle  as  shown  in  Fig.  2. 

In  Fig.  3 , divide  A B and  A D into  eight  parts,  each  length 
being  1 inch.  Through  the  points  H,  I,  J,  K,  L,  M and  N draw 
vertical  lines  with  the  triangle.  Through  O,  P,  Q,  R,  S,  T and  U 
draw  horizontal  lines  with  the  T-square.  Now  draw  lines  con- 
necting O and  H,  P and  I,  Q and  J,  etc.  These  lines  can  be 
drawn  with  the  45-degree  triangle,  as  they  form  an  angle  of  45 
degrees  with  the  horizontal.  Starting  at  N draw  lines  from  A B 
to  B C at  an  angle  of  45  degrees.  Also  draw  lines  from  A D to 
D C through  the  points  O,  P,  Q,  R,  etc.,  forming  angles  of  45 
degrees  with  D C. 

Fig . ^ is  drawn  with  the  compasses.  First  draw  the  diagonals 
A C and  D B.  With  the  T-square  draw  the  line  E H.  Now 
mark  off  on  E H distances  of  | inch.  With  the  compasses  set  so 
that  the  point  of  the  lead  is  2 inches  from  the  needle  point,  de- 
scribe the  circle  passing  through  E.  Witli  H as  a center  draw 
the  arcs  F G and  I J having  a radius  of  1|  inches.  In  drawing 
these  arcs  be  careful  not  to  go  beyond  the  diagonals,  but  stop  at 
the  points  F and  G and  I and  J.  Again  with  H as  the  center 
and  a radius  of  li  inches  draw  a circle.  The  arcs  K L and  M N 
are  drawn  in  the  same  manner  as  were  arcs  F G and  I J ; tha 


44 


PLATE 


JANUARY*  /A,  / 90/.  HELP  BURT  U HA  NHL  BP  CH/BAOO, 


MECHANICAL  DRAWING. 


37 


radius  being  li  inches.  Now  draw  circles,  with  H as  the  center, 
of  1,  -J,  | and  ^ inch  radius,  passing  through  the  points  P,  T,  etc. 

Fig.  5 is  an  exercise  with  the  line  pen  and  compasses.  First 
draw  the  diagonals  A C and  D B,  the  horizontal  line  L M and  the 
vertical  line  E F passing  through  the  center  Q.  Mark  off  dis- 
tances of  1 inch  on  L M and  E F and  draw  the  lines  NN' O O' 
and  N R,  O S,  etc.,  through  these  points,  forming  the  squares 
N R R'N',  O S S'  O',  etc.  With  the  bow  pencil  adjusted  so 
that  the  distance  between  the  pencil  point  and  the  needle  point  is 
1 inch  draw  the  arcs  having  centers  at  the  corners  of  the  squares. 
The  arc  whose  center  is  N will  be  tangent  to  the  lines  A L and 
A E and  the  arc  whose  center  is  O will  be  tangent  to  N N'  and 
N R.  Since  P T,  T T',  T'  P'  and  P'  P are  each  1 inch  long  and 
form  the  square,  the  arcs  drawn  with  Q as  a center  will  form  a 
circle. 

To  draw  Fig.  6 , first  draw  the  center  lines  E F and  L M. 
Now  find  the  centers  of  the  small  squares  A L I E,  L B F I etc. 
Through  the  center  I draw  the  construction  lines  HIT  and 
RIP  forming  angles  of  30  degrees  with  the  horizontal.  Now 
adjust  the  compasses  to  draw  circles  having  a radius  of  one  inch. 
With  I as  a center,  draw  the  circle  H P T R.  With  the  same 
radius  (one  inch  V draw  the  arcs  with  centers  at  A,  B,  C and 
D.  Also  draw  the  semi-circles  with  centers  at  L,  F,  M and  E. 
Now  draw  the  arcs  as  shown  having  centers  at  the  centers  of  the 
small  squares  A L I E,  L B F I,  etc.  To  locate  the  centers  of 
the  six  small  circles  within  the  circle  H P T R,  draw  a circle 
with  a radius  of  -A  inch  and  having  the  center  in  I.  The  small 
circles  have  a radius  of  -A-  inch. 

Inking.  In  inking  this  plate,  the  outlines  of  the  squares  of 
the  various  figures  are  inked  only  in  Figs.  2 and  3.  In  Fig.  1 the 
only  lines  to  be  inked  are  those  shown  in  full  lines  in  PLATE 
III.  First  ink  the  star  and  then  the  square  and  diamonds.  The 
cross  hatching  should  be  done  ivithout  measuring  the  distance  be- 
tween the  lines  and  without  the  aid  of  any  cross  hatching  device 
as  this  is  an  exercise  for  practice.  The  lines  should  be  about  -A 
inch  apart.  After  inking ’erase  all  construction  lines. 

In  inking  Fig.  2 be  careful  not  to  run  over  lines.  Each 
line  should  coincide  with  the  pencil  line.  The  student  should 


47 


38 


MECHANICAL  DRAWING. 


first  ink  the  horizontal  lines  L,  M and  N and  the  vertical  lines 
E,  F and  G.  The  short  lines  should  have  the  same  width 
but  the  border  lines,  A B,  B C,  C D and  D A should  be  a 
little  heavier. 

Fig.  3 is  drawn  entirely  with  the  45-degree  triangle.  In  ink- 
ing the  oblique  lines  make  F I,  R K,  T M,  etc.,  a light  distinct 
line.  The  alternate  lines  O II,  Q J,  S L,  etc.,  should  be  some- 
what heavier.  All  of  the  lines  which  slope  in  the  opposite  direc- 
tion are  light.  After  inking  Fig.  3 all  horizontal  and  vertical 
lines  (except  the  border  lines)  should  be  erased.  The  border 
lines  should  be  slightly  heavier  than  the  light  oblique  lines. 

The  only  instrument  used  in  inking  Fig.  4 is  the  compasses. 
In  doing  this  exercise  adjust  the  legs  of  the  compasses  so  that  the 
pen  will  always  be  perpendicular  to  the  paper.  If  this  is  not 
. done  both  nibs  will  not  touch  the  paper  and  the  line  will  be  ragged. 
In  inking  the  arcs,  see  that  the  pen  stops  exactly  at  the  diagonals. 
The  circle  passing  through  T and  the  small  inner  circle  should  be 
dotted  as  shown  in  PLATF  III.  After  inking  the  circles  and 
arcs  erase  the  construction  lines  that  are  without  the  outer  circles 
but  leave  in  pencil  the  diagonals  inside  the  circle. 

In  Fig.  5 draw  all  arcs  first  and  then  draw  the  straight  lines 
meeting  these  arcs.  It  is  much  easier  to  draw  straight  lines  meet- 
ing  arcs,  or  tangent  to  them,  than  to  make  the  arcs  tangent  to 
straight  lines.  As  this  exercise  is  difficult,  and  in  all  mechanical 
and  machine  drawing  arcs  and  tangents  are  frequently  used  we 
advise  the  beginner  to  draw  this  exercise  several  times.  Leave 

O 

all  construction  lines  in  pencil. 

Fig.  6 , like  Fig.  4 , is  an  exercise  with  compasses.  If  Fig.  6 
has  been  laid  out  accurately  in  pencil,  the  inked  arcs  will  be  tan- 
gent to  each  other  and  the  finished  exercise  will  have  a good 
appearance.  If,  however,  the  distances  were  not  accurately 
measured  and  the  lines  carefully  drawn  the  inked  arcs  will  not  be 
tangent.  The  arcs  whose  centers  are  L,  F,  M and  E and  A,  B,  C 
and  D should  be  heavier  than  the  rest.  The  small  circles  may  be 
drawn  with  the  bow  pen.  After  inking  the  arcs  all  construction 
lines  should  be  erased. 


48 


DETAILS  * OF*  IONIC*  CAPITAL 


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A Study  in  Orthographic  Projection. 


MECHANICAL  DRAWING, 


PART  II. 

GEOHETRICAL  DEFINITIONS. 

A point  is  used  for  marking  position  ; it  lias  neither  iengtli 
breadth  nor  thickness. 

A line  has  length  only ; it  is  produced  by  the  motion  of  a 
point. 

A straight  line  or  right  line  is  one  that  has  the  same  direction 
throughout.  It  is  the  shortest  distance  between  any  two  of  its 
points. 

A curved  line  is  one  that  is  constantly  changing  in  direction. 
It  is  sometimes  called  a curve. 

A broken  line  is  one  made  up  of  several  straight  lines. 

Parallel  lines  are  equally  distant  from  each  other  at  all 
points. 

A horizontal  line  is  one  having  the  direction  of  a line  drawn 
upon  the  surface  of  water  that  is  at  rest.  It  is  a line  parallel  to 
the  horizon. 

A vertical  line  is  one  that  lies  in  the  direction  of  a thread 
suspended  from  its  upper  end  and  having  a weight  at  the  lower 
end.  It  is  a line  that  is  perpendicular  to  a horizontal  plane. 

Lines  are  perpendicular  to  each  other,  if  when  they  cross, 
the  four  angles  formed  are  equal.  If  they  meet  and  form  two 
equal  angles  they  are  perpendicular. 

An  oblique  line  is  one  that  is  neither  vertical  nor  horizontals 

In  Mechanical  Drawing,  lines  drawn  along  me  edge  of  the 
T square,  when  the  head  of  the  T square  is  resting  against  the 
left-hand  edge  of  the  board,  are  called  horizontal  lines.  Those 
drawn  at  right  angles  or  perpendicular  to  the  edge  of  the  T square 
are  called  vertical. 

If  two  lines  cut  each  other,  they  are  called  intersecting  lines , 
and  the  point  at  which  they  cross  is  called  the  point  of  intersection. 


51 


4 


MECHANICAL  DRAWING. 


ANGLES. 

An  angle  is  formed  when  two  straight  lines  meet.  An  angle 
is  often  defined  as  being  the  difference  in  direction  of  two  straight 
lines.  The  lines  are  called  the  sides  and  the  point  of  meeting  is 
called  the  vertex . The  size  of  an  angle  depends  upon  the  amount 
of  divergence  of  the  sides  and  is  independent  of  the  length  of 
these  lines. 

Y_ 


RIGHT  ANGLE.  ACUTE  ANGLE.  OBTUSE  ANGLE. 

If  one  straight  line  meet  another  and  the  angles  thus  formed 
are  equal  they  are  right  angles.  When  two  lines  are  perpendic- 
ular to  each  other  the  angles  formed  are  right  angles. 

An  acute  angle  is  less  than  a right  angle. 

An  obtuse  angle  is  greater  than  a right  angle. 

SURFACES. 

A surface  is  produced  by  the  motion  of  a line;  it  has  two 
dimensions,  — length  and  breadth. 

A plane  figure  is  a plane  bounded  on  all  sides  by  lines ; the 
space  included  within  these  lines  (if  they  are  straight  lines)  is 
called  a polygon  or  a rectilinear  figure, 

TRIANGLES. 

A triangle  is  a figure  enclosed  by  three  straight  lines.  It  is 
a potygon  of  three  sides.  The  bounding  lines  are  the  sides,  and 
the  points  of  intersection  of  the  sides  are  the  vertices.  The  angles 
of  a triangle  are  the  angles  formed  by  the  sides. 

A right-angled  triangle,  often  called  a right  triangle,  is  one 
that  has  a right  angle. 

An  acute-angled  triangle  is  one  that  has  all  of  its  angles  acute. 

An  obtuse-angled  triangle  is  one  that  has  an  obtuse  angle. 

In  an  equilateral  triangle  all  of  the  sides  are  equal. 


52 


MECHANICAL  DRAWING. 


5 


If  all  of  the  angles  of  a triangle  are  equal,  the  figure  is  called 

an  equiangular  triangle. 

A triangle  is  called  scalene,  when  no  two  of  its  sides  are 
equal. 

In  an  isosceles  triangle  two  of  the  sides  are  equal. 


RIGHT  ANGLED  TRIANGLE.  ACUTE  ANGLED  TRIANGLE.  OBTUSE  ANGLED  TRIANGLE. 


The  base  of  a triangle  is  the  lowest  side  ; however,  any  side 
may  be  taken  as  the  base.  In  an  isosceles  triangle  the  side  which 
is  not  one  of  the  equal  sides  is  usually  considered  the  base. 

The  altitude  of  a triangle  is  the  perpendicular  drawn  from 
the  vertex  to  the  base. 


EQUILATERAL  TRIANGLE. 


ISOSCELES  TRIANGLE. 


SCALENE  TRIANGLE. 


QUADRILATERALS. 

A quadrilateral  is  a plane  figure  bounded  by  four  straight 

lines. 

The  diagonal  of  a quadrilateral  is  a straight  line  joining  two 
opposite  vertices. 


A trapezium  is  a quadrilateral,  no  two  of  whose  sides  are 
parallel. 

A trapezoid  is  a quadrilateral  having  two  sides  parallel. 


53 


6 


MECHANICAL  DRAWING. 


The  bases  of  a trapezoid  are  its  parallel  sides.  The  altitude 
is  the  perpendicular  distance  between  the  bases. 

A parallelogram  is  a quadrilateral  whose  opposite  sides  are 
parallel. 

The  altitude  of  a parallelogram  is  the  perpendicular  distance 
between  the  bases  which  are  the  parallel  sides. 

There  are  four  kinds  of  parallelograms: 


RECTANGLE.  SQUARE.  RHOMBUS. 

A rectangle  is  a parallelogram,  all  of  whose  angles  are  right 
angles.  The  opposite  sides  are  equal. 

A square  is  a rectangle,  all  of  whose  sides  are  equal. 

A rhombus  is  a parallelogram  which  has  four  equal  sides; 
but  the  angles  are  not  right  angles. 

A rhomboid  is  a parallelogram  whose  adjacent  sides  are 
unequal ; the  angles  are  not  right  angles. 

POLYGONS. 

A polygon  is  a plane  figure  bounded  by  straight  lines. 

The  boundary  lines  are  called  the  sides  and  the  sum  of  the 
sides  is  called  the  perimeter . 

Polygons  are  classified  according  to  the  number  of  sides. 

A triangle  is  a polygon  of  three  sides. 

A quadrilateral  is  a polygon  of  four  sides. 

A pentagon  is  a polygon  of  five  sides. 

A hexagon  is  a polygon  of  six  sides. 

A heptagon  is  a polygon  of  seven  sides. 

An  octagon  is  a polygon  of  eight  sides. 

A decagon  is  a polygon  of  ten  sides. 

A dodecagon  is  a potygon  of  twelve  sides. 

An  equilateral  polygon  is  one  all  of  whose  sides  are  equal. 

An  equiangular  polygon  is  one  all  of  whose  angles  are  equal. 
A regular  polygon  is  one  all  of  whose  angles  are  equal  and  all 
of  whose  sides  are  equal. 


54 


MECHANICAL  DRAWING. 


7 


CIRCLES. 

A circle  is  a plane  figure  bounded  by  a curved  line,  every  point 
of  which  is  equally  distant  from  a point  within  called  the  center. 

The  curve  which  bounds  the  circle  is  called  the  circumference. 
Any  portion  of  the  circumference  is  called  an  arc. 

The  diameter  of  a circle  is  a straight  line  drawn  through  the 
center  and  terminating  in  the  circumference.  A radius  is  a 
straight  line  joining  the  center  with  the  circumference.  It  has  a 
length  equal  to  one  half  the  diameter.  All  radii  (plural  of 
radius)  are  equal  and  all  diameters  are  equal  since  a diameter 
equals  two  radii. 

O 

PENTAGON.  HEXAGON.  OCTAGON. 


An  arc  equal  to  one-half  the  circumference  is  called  a semi- 
circumferenceand  an  arc  equal  to  one-quarter  of  the  circumfer- 
ence is  called  a quadrant . A quadrant  may  mean  the  sector,  arc 
or  angle. 

A chord  is  a straight  line  joining  the  extremities  of  an  arc. 
It  is  a line  drawn  across  a circle  that  does  not  pass  through  the 
center. 

A secant  is  a straight  line  which  intersects  the  circumference 
in  two  points. 


A tangent  is  a straight  line  which  touches  the  circumference 
at  only  one  point.  It  does  not  intersect  the  circumference.  The 
point  at  which  the  tangent  touches  the  circumference  is  called  the 
point  of  tangency  or  point  of  contact . 


55 


8 


MECHANICAL  DRAWING. 


A sector  of  a circle  is  the  portion  or  area  included  between 
an  arc  and  two  radii  drawn  to  the  extremities  of  the  arc. 

A segment  of  a circle  is  the  area  included  between  an  arc 
and  its  chord. 


Circles  are  tangent  when  the  circumferences  touch  at  only- 
one  point  and  are  concentric  when  they  have  the  same  center. 


CONCENTRIC  CIRCLES.  INSCRIBED  POLYGON 


An  inscribed  angle  is  an  angle  whose  vertex  lies  in  the  cir- 
cumference and  whose  sides  are  chords.  It  is  measured  by  one- 
half  the  intercepted  arc. 

A central  angle  is  an  angle  whose  vertex  is  at  the  center  of 
the  circle  and  whose  sides  are  radii. 


An  inscribed  polygon  is  one  whose  vertices  lie  in  the  circum- 
ference and  whose  sides  are  chords. 


MEASUREnENT  OF  ANGLES. 

To  measure  an  angle  describe  an  arc  with  the  center  at  the 
vertex  of  the  angle  and  having  any  convenient  radius.  The  por- 
tion of  the  arc  included  between  the  sides  of  the  angle  is  the 
measure  of  the  angle.  If  the  arc  has  a constant  radius  the  greater 
the  divergence  of  the  sides,  the  longer  will  be  the  arc.  If  there 
are  several  arcs  drawn  with  the  same  center,  the  intercepted  arcs 
will  have  different  lengths  but  they  will  all  be  the  same  fraction 
of  the  entire  circumference. 

In  order  that  the  size  of  an  angle  or  arc  may  be  stated  with- 


56 


MECHANICAL  DRAWING. 


9 


out  saying  that  it  is  a certain  fraction  of  a circumference,  the  cir- 
cumference is  divided  into  360 
equal  parts  called  degrees.  Thus 
we  can  say  that  an  angle  contains 
45  degrees,  which  means  that  it  is 
^g5-Q  = | of  a circumference.  In 
order  to  obtain  accurate  measure- 
ments each  degree  is  divided  into 
60  equal  parts  called  minutes  and 
each  minute  is  divided  into  60  equal 
parts  called  seconds.  Angles  and 
arcs  are  usually  measured  by  means  of  an  instrument  called  a 
protractor  which  has  already  been  explained. 

SOLIDS. 

A polyedron  is  a solid  bounded  by  planes.  The  bounding 
planes  are  called  the  faces  and  their  intersections  edges.  The 
intersections  of  the  edges  are  called  vertices. 

A polygon  having  four  faces  is  called  a tetraedron ; one  having 
six  faces  a hexaedron  ; of  eight  faces  an  octaedron ; of  twelve 
faces  a dodecaedron,  etc. 


PRISM.  RIGHT  PRISM.  TRUNCATED  PRISM. 

A prism  is  a polyedron,  of  which  two  opposite  faces,  called 
bases,  are  equal  and  parallel ; the  other  faces,  called  lateral  faces 
are  parallelograms. 

The  area  of  the  lateral  faces  is  called  the  lateral  area. 

The  altitude  of  a prism  is  the  perpendicular  distance  between 
the  bases. 

Prisms  are  triangular , quadrangular , etc.,  according  to  the 
shape  of  the  base. 

A right  prism  is  one  whose  lateral  edges  are  perpendicular 
to  the  bases. 


57 


10 


MECHANICAL  DRAWING. 


A regular  prism  is  a right  prism  having  regular  polygons  for 
bases. 

A parallelopiped  is  a prism  whose  Bases  are  parallelograms. 
If  the  edges  are  all  perpendicular  to  the  bases  it  is  called  a right 
parallelopiped. 

A rectangular  parallelopiped  is  a right  parallelopiped  whose 

bases  are  rectangles  ; all  the  faces  are  rectangles. 

0 

PARALLELOPIPED.  RECTANGULAR  PARALLELOPIPED.  OCTAEDRON. 

A cube  is  a rectangular  parallelopiped  all  of  whose  faces  are 
squares. 

A truncated  prism  is  the  portion  of  a prism  included  between 
the  base  and  a plane  not  parallel  to  the  base. 


PYRAMIDS. 

A pyramid  is  a polyedron  one  face  of  which  is  a polygon 
(called  the  base)  and  the  other  faces  are  triangles  having  a com- 
mon vertex. 


PYRAMID. 


REGULAR  PYRAMID. 


FRUSTUM  OF  PYRAMID. 


The  vertices  of  the  triangles  form  the  vertex  of  the  pyramid. 
The  altitude  of  the  pyramid  is  the  perpendicular  distance 
from  the  vertex  to  the  base. 

A pyramid  is  called  triangular,  quadrangular,  etc.,  accord- 
ing to  the  shape  of  the  base. 

A regular  pyramid  is  one  whose  base  is  a regular  polygon 


58 


MECHANICAL  DRAWING. 


11 


and  whose  vertex  lies  in  the  perpendicular  erected  at  the  center 
of  the  base. 

A truncated  pyramid  is  the  portion  of  a pyramid  included 
between  the  base  and  a plane  not  parallel  to  the  base. 

A frustum  of  a pyramid  is  the  solid  included  between  the 
base  and  a plane  parallel  to  the  base. 

The  altitude  of  a frustum  of  a pyramid  is  the  perpendicular 
distance  between  the  bases. 

CYLINDERS. 

A cylindrical  surface  is  a curved  surface  generated  by  the 
motion  of  a straight  line  which  touches  a curve  and  continues 
parallel  to  itself. 

A cylinder  is  a solid  bounded  by  a cylindrical  surface  and 
two  parallel  planes  intersecting  this  surface. 

The  parallel  faces  are  called  bases. 

Q 

CYLINDER.  RIGHT  CYLINDER.  INSCRIBED  CYLINDER. 

The  altitude  of  a cylinder  is  the  perpendicular  distance 
between  the  bases. 

A circular  cylinder  is  a cylinder  whose  base  is  a circle. 

A right  cylinder  or  a cylinder  of  revolution  is  a cylinder  gen- 
erated by  the  revolution  of  a rectangle  about  one  side  as  an  axis. 

A prism  whose  base  is  a regular  polygon  may  be  inscribed  in 
or  circumscribed  about  a circular  cylinder. 

The  cylindrical  area  is  call  the  lateral  area.  The  total  area 
is  the  area  of  the  bases  added  to  the  lateral  area. 

CONES. 

A conical  surface  is  a curved  surface  generated  by  the 
motion  of  a straight  line,  one  point  of  which  is  fixed  and  the  end 
or  ends  of  which  move  in  a curve. 


59 


12 


MECHANICAL  DRAWING. 


A cone  is  a solid  bounded  by  a conical  surface  and  a plane 
which  cuts  the  conical  surface. 

The  plane  is  called  the  base  and  the  curved  surface  the 
lateral  area. 

The  vertex  is  the  fixed  point. 

The  altitude  of  a cone  is  the  perpendicular  distance  from  the 
vertex  to  the  base. 

An  element  of  a cone  is  a straight  line  from  the  vertex  to  the 
perimeter  of  the  base. 

A circular  cone  is  a cone  whose  base  is  a circle. 


CONE. 


A right  circular  cone  or  cone  of  revolution  is  a cone  whose 
axis  is  perpendicular  to  the  base.  It  may  be  generated  by  the 
revolution  of  a right  triangle  about  one  of  the  perpendicular  sides 
as  an  axis. 

A frustum  of  a cone  is  the  solid  included  between  the  base 
and  a plane  parallel  to  the  base. 


The  altitude  of  a frustum  of  a cone  is  the  perpendicular 
distance  between  the  bases. 

SPHERES. 


A sphere  is  a solid  bounded  by  a curved  surface,  every  point 
of  which  is  equally  distant  from  a point  within  called  the  center. 
The  radius  of  a sphere  is  a straight  line  drawn  from  the 


60 


MECHANICAL  DRAWING 


13 


center  to  the  surface.  The  diameter  is  a straight  line  drawn 
through  the  center  and  having  its  extremities  in  the  surface. 

A sphere  may  be  generated  by  the  revolution  of  a semi-circle 
about  its  diameter  as  an  axis. 

An  inscribed  polyedron  is  a polyedron  whose  vertices  lie  in 
the  surface  of  the  sphere. 

An  circumscribed  polyedron  is  a polyedron  whose  faces  are 
tangent  to  a sphere. 

A great  circle  is  the  intersection  of  the  spherical  surface  and 
a plane  passing  through  the  center  of  a sphere. 

A small  circle  is  the  intersection  of  the  spherical  surface  and 
a plane  which  does  not  pass  through  the  center. 

A sphere  is  tangent  to  a plane  when  the  plane  touches  the 
surface  in  only  one  point.  A plane  perpendicular  to  the  extremity 
of  a radius  is  tangent  to  the  sphere. 


CONIC  SECTIONS. 

If  a plane  intersects  a cone  the  geometricrd  figures  thus 
formed  are  called  conic  sections.  A plane  perpendicular  to  the 
base  and  passing  through  the  vertex  of  a right  circular  cone  forms 
an  isosceles  triangle.  If  the  plane  is  parallel  to  the  base  the 
intersection  of  the  plane  and  conical  surface  will  be  the  circum- 
ference of  a circle. 


Fig.  1.  Fig.  2.  Fig.  3.  Fig.  4. 

Ellipse.  The  ellipse  is  a curve  formed  by  the  intersection  of 
a plane  and  a cone,  the  plane  being  oblique  to  the  axis  but  not 
cutting  the  base.  If  a plane  is  passed  through  a cone  as  shown 
in  Fig.  1 or  through  a cylinder  as  shown  in  Fig  2,  the  curve  of 
intersection  will  be  an  ellipse.  An  ellipse  may  be  defined  as 
being  a curve  generated  by  a point  moving  in  a plane , the  sum  of 
the  distances  of  the  point  to  two  fixed  points  being  always  constant . 

The  two  fixed  points  are  called  the  foci  and  lie  on  the 


01 


14 


MECHANICAL  DRAWING. 


longest  line  that  can  be  drawn  in  the  ellipse.  One  of  these  points 
is  called  a focus . 

The  longest  line  that  can  be  drawn  in  an  ellipse  is  called  the 
major  axis  and  the  shortest  line,  passing  through  the  center,  is 
called  the  minor  axis.  The  minor  axis  is  perpendicular  to  the 
middle  point  of  the  major  axis  and  the  point  of  intersection  is 
called  the  center 

An  ellipse  may  be  constructed  if  the  major  and  minor  axes 
are  given  or  if  the  foci  and  one  axis  are  known. 


VERTEX 


ELLIPSE.  PARABOLA. 

Parabola.  The  parabola  is  a curve  formed  by  the  inter- 
section of  a cone  and  a plane  parallel  to  an  element  as  shown  in. 
Fig.  3.  The  curve  is  not  a closed  curve.  The  branches  approach 
parallelism. 

A parabola  may  be  defined  as  being  a curve  every  point  of 

which  is  equally  distayd  from  a line 
and  a point. 

The  point  is  called  the  focus  and 
the  given  line  the  directrix.  The 
line  perpendicular  to  the  directrix 

and  passing  through  the  focus  is 

the  axis.  The  intersection  of  the 
axis  and  the  curve  is  the  vertex. 

Hyperbola.  This  curve  is  formed 
by  the  intersection  of  a plane  and  a cone,  the  plane  being  parallel 

to  the  axis  of  the  cone  as  shown  in  Fig.  4.  Like  the  parabola, 

the  curve  is  not  a closed  curve ; the  branches  constantly  diverge. 

An  hyperbola  is  defined  as  being  a plane  curve  such  that  the 
difference  of  the  distances  from  any  point  in  the  curve  to  two  fixed 
points  is  equal  to  a given  distance . 


62 


MECHANICAL  DRAWING. 


15 


The  two  fixed  points  are  the  foci  and  the  line  passing  through 
them  is  the  transverse  axis. 

Rectangular  Hyperbola.  The  form  of  hyperbola  most  used 
in  Mechanical  Engineering  is  called  the  rectangular  hyperbola 
because  it  is  drawn  with  reference  to  rectangular  co-ordinates. 
This  curve  is  constructed  as  follows  : In  Fig.  5,  O X and  O Y are 
the  two  co-ordinates  drawn  at  right  angles  to  each  other.  These 
lines  are  also  called  axes  or 
asymptotes.  Assume  A to 
be  a known  point  on  the 
curve.  In  drawing  this  curve 
for  the  theoretical  indicator 
card,  this  point  A is  the  point 
of  cut-off. 

Draw  A C parallel  to 
O X and  A D perpendicular 
to  O X.  Now  mark  off  any 
convenient  points  on  A C such  as  E,  F,  G,  and  H ; and  through 
these  points  draw  EE',  FF',  GG',  and  II IF  perpendicular  to  O X. 
Connect  E,  F,  G,  H and  C with  O.  Through  the  points  of  inter- 
section of  the  oblique  lines  and  the  vertical  line  AD  draw  the 
horizontal  lines  LL',  MM',  NN',  PP'  and  QQ'.  The  first  point  on 
the  curve  is  the  assumed  point  A,  the  second  point  is  R,  the 
intersection  of  LL'  and  EE'.  The  third  is  the  intersection  S 
of  MM'  and  FF';  the  fourth  is  the  intersection  T of  NN'  and 
GG'.  The  other  points  are  found  in  the  same  way. 

In  this  curve  the  products  of  the  co-ordinates  of  all  points  are 
equal.  Thus  LR  X RE'  = MS  X SF'=  NT  X TG'. 

ODONTOIDAL  CURVES. 

The  outlines  of  the  teeth  of  gears  must  be  drawn  accurately 
because  the  smoothness  of  running  depends  upon  the  shape  of  the 
teeth.  The  two  classes  of  curves  generally  employed  in  drawing 
gear  teeth  are  the  cycloidal  and  involute. 

Cycloid.  The  cycloid  is  a curve  generated  by  a point  on  the 
circumference  of  a circle  which  rolls  on  a straight  line  tangent  to 
the  circle. 

The  rolling  circle  is  called  the  describing  or  generating  circle 


Y ,4  E r o H c 


03 


1G 


MECHANICAL  DRAWING. 


and  the  point,  the  describing  or  generating  point.  The  tangent 
alongf  which  the  circle  rolls  is  called  the  director. 

O 

In  order  that  the  curve  may  be  a true  cycloid  the  circle  must 
roll  without  any  slipping. 


Epicycloid.  If  the  generating  circle  rolls  upon  the  outside 
of  an  arc  or  circle,  called  the  director  circle , the  curve  thus  gener- 
ated is  called  an  epicycloid.  The  method  of  drawing  this  curve 
is  the  same  as  that  for  the  cycloid. 

Hypocycloid.  In  case  the  generating  circle  rolls  upon  the 
inside  of  an  arc  or  circle,  the  curve  thus  generated  is  called  the 
hypocycloid.  The  circle  upon  which  the  generating  circle  rolls  is 


called  the  director  circle.  If  the  generating  circle  has  a diameter 
equal  to  the  radius  of  the  director  circle  the  hypocycloid  becomes 
a straight  line. 

Involute.  If  a thread  or  fine  wire  is  wound  around  a 
cylinder  or  circle  and  then  unwound,  the  end  will  describe  a 
curve  called  an  involute.  The  involute  may  be  defined  as  being 
a curve  generated  by  a point  in  a tangent  rolling  on  a circle  known 
as  the  base  circle. 

The  construction  of  the  ellipse,  parabola,  hyperbola  and 
odontoidal  curves  will  be  taken  up  in  detail  with  the  plates. 


64 


MECHANICAL  DRAWING. 


17 


PLATE  IV. 

Pencilling.  The  horizontal  and  vertical  center  lines  and  the 
border  lines  for  PLATE  IV  should  l:e  laid  out  in  the  same 
manner  as  were  those  for  PLATE  I.  There  are  to  be  six  figures 
on  this  plate  and  to  facilitate  the  laying  out  of  the  work,  the  fol- 
lowing lines  should  be  drawn : measure  off  inches  on  botli  sides 
of  the  vertical  center  line  and  through  these  points  draw  vertical 
lines  as  shown  in  dot  and  dash  lines  on  PLATE  IV  In  these 
six  spaces  the  six  figures  are  to  be  drawn,  the  student  placing 
them  in  the  centers  of  the  spaces  so  that  they  will  present  a good 
appearance.  In  locating  the  figures,  they  should  be  placed  a little 
above  the  center  so  that  there  will  be  sufficient  space  below  to 
number  the  problem. 

The  figures  of  the  problems  should  first  be  drawn  lightly  in 
pencil  and  after  the  entire  plate  is  completed  the  lines  should  be 
inked.  In  pencilling,  all  intersections  must  be  formed  with  great 
care  as  the  accuracy  of  the  results  depends  upon  the  pencilling. 
Keep  the  pencil  points  in  good  order  at  all  times  and  draw  lines 
exactly  through  intersections. 

GEOMETRICAL  PROBLEMS. 

The  following  problems  are  of  great  importance  to  the 
mechanical  draughtsman.  The  student  should  solve  them  with 
care ; he  should  not  do  them  blindly,  but  should  understand  them 
so  that  he  can  apply  the  principles  in  later  work. 

PROBLEM  I.  To  Bisect  a Given  Straight  Line. 

Draw  the  horizontal  straight  line  A G about  3 inches  long. 
With  the  extremity  A as  a center  and  any  convenient  radius 
(about  2 inches)  describe  arcs  above  and  below  the  line  A C. 
With  the  other  extremity  C as  a center  and  with  the  same  radius 
draw  short  arcs  above  and  below  A C intersecting  the  first  arcs  at 
D and  E.  The  radius  of  these  arcs  must  be  greater  than  one-half 
the  length  of  the  line  in  order  that  they  may  intersect.  Now 
draw  the  straight  line  D E passing  through  the  intersections  D 
and  E.  This  line  cuts  the  line  A C at  F which  is  the  middle 
point. 

A F = F C 


65 


18 


MECHANICAL  DRAWING. 


Proof.  Since  the  points  D and  E are  equally  distant  from 
A and  C a straight  line  drawn  through  them  is  perpendicular  to 
A C at  its  middle  point  F. 

PROBLEM  2.  To  Construct  an  Angle  Equal  to  a Given 
Angle. 

Draw  the  line  O C about  2 inches  long  and  the  line  O A of 
about  the  same  length.  The  angle  formed  by  these  lines  may  be 
any  convenient  size  (about  45  degrees  is  suitable).  This  angle 
A O C is  the  given  angle. 

Now  draw  F G a horizontal  line  about  2L  inches  long  and  let 
F the  left-hand  extremity  be  the  vertex  of  the  angle  to  be 
constructed. 

With  O as  a center  and  any  convenient  radius  (about  1| 
inches)  describe  the  arc  L M cutting  both  O A and  OC.  With 
F as  a center  and  the  same  radius  draw  the  indefinite  arc  O Q. 
Now  set  the  compass  so  that  the  distance  between  the  pencil  and 
the  needle  point  is  equal  to  the  chord  L M.  With  Q as  a center 
and  a radius  equal  to  L M draw  an  arc  cutting  the  arc  O Q at  P. 
Through  F and  P draw  the  straight  line  F E.  The  angle  EF  G 
is  the  required  angle  since  it  is  equal  to  A O C. 

Proof.  Since  the  chords  of  the  arcs  L M and  P Q are  equal 
the  arcs  are  equal.  The  angles  are  equal  because  with  equal 
radii  equal  arcs  are  intercepted  by  equal  angles. 

PROBLEM  3.  To  Draw  Through  a Given  Point  a Line 
Parallel  to  a Given  Line. 

First  Method.  Draw  the  horizontal  straight  line  A C about 
3|  inches  long  and  assume  the  point  P about  It  inches  above 
A C.  Through  the  point  P draw  an  oblique  line  F E forming 
any  convenient  angle  with  A C.  (Make  the  angle  about  60 
degrees).  Now  construct  an  angle  equal  to  P F C having  the 
vertex  at  P and  one  side  the  line  E P.  (See  problem  2). 
This  may  be  done  as  follows:  With  F as  a center  and  any  con- 
venient radius,  describe  the  arc  L M.  With  the  same  radius 
draw  the  indefinite  arc  N O using  P as  the  center.  With  N as  a 
center  and  a radius  equal  to  the  chord  L M,  draw  an  arc  cutting 
the  arc  N O at  O.  Through  the  points  P and  O draw  a straight 
line  which  will  be  parallel  to  A C. 


66 


plate: 


V"  /^.  /0O/.  /-y^r/=?^yEr/=?7r‘  £?/-/^\A/-Z7/LjE~^?  Z7/V/<03  £?£?,  //L/L. 


MECHANICAL  DRAWING. 


19 


Proof.  If  two  straight  lines  are  cut  by  a third  making  the 
corresponding  angles  equal,  the  lines  are  parallel. 

PROBLEM  4.  To  Draw  Through  a Given  Point  a Line 
Parallel  to  a Given  Line. 

Second  Method.  Draw  the  straight  line  A C about  3L  inches 
long  and  assume  the  point  P about  IT  inches  above  A C.  With 
P as  a center  and  any  convenient  radius  (about  21  inches)  draw 
the  indefinite  arc  E D cutting  the  line  A C.  Now  with  the  same 
radius  and  with  D as  a center,  draw  an  arc  P Q.  Set  the  com- 
pass so  that  the  distance  between  the  needle  point  and  the  pencil 
is  equal  to  the  chord  P Q.  With  D as  a center  and  a radius 
equal  to  P Q,  describe  an  arc  cutting  the  arc  E D at  H.  A line 
drawn  through  P and  H will  be  parallel  to  A C. 

Proof.  Draw  the  line  Q H.  Since  the  arcs  P Q and  II  D 
are  equal  and  have  the  same  radii,  the  angles  P H Q and  H Q D 
are  equal.  Two  lines  are  parallel  if  the  alternate  interior  angles 
are  equal. 

PROBLEM  5.  To  Draw  a Perpendicular  to  a Line  from 
a Point  in  the  Line. 

First  Method.  When  the  point  is  near  the  middle  of  the  line. 

Draw  the  horizontal  line  A C about  3^  inches  long  and 
assume  the  point  P near  the  middle  of  the  line.  With  P as  a 
center  and  any  convenient  radius  (about  1^  inches)  draw  two  arcs 
cutting  the  line  A C at  E and  F.  Now  with  E and  F as  centers 
and  any  convenient  radius  (about  2L  inches)  describe  arcs  inter- 
secting at  O.  The  line  O P will  be  perpendicular  to  A C at  P. 

Proof.  The  points  P and  O are  equally  distant  from  E and 
F.  Hence  a line  drawn  through  them  is  perpendicular  to  the 
middle  point  of  E F which  is  P. 

PROBLEM  6.  To  Draw  a Perpendicular  to  a Line  from 
a Point  in  the  Line. 

Second  Method . When  the  point  is  near  the  end  of  the  line. 

Draw  the  line  A C about  3J  inches  long.  Assume  the  given 
point  P to  be  about  ^ inch  from  the  end  A.  With  any  point  D 
as  a center  and  a radius  equal  to  D P,  describe  an  arc,  cutting  A C 
at  E.  Through  E and  D draw  the  diameter  E O.  A line  from 
O to  P is  perpendicular  to  A C at  P. 


69 


20 


MECHANICAL  DRAWING. 


Proof.  The  angle  O P E is  inscribed  in  a semi-circle ; hence 
it  is  a right  angle,  and  the  sides  O P and  P E are  perpendicular 
to  each  other. 

After  completing  these  figures  draw  pencil  lines  for  the 
lettering.  The  words  “ PLATE  IV"  and  the  date  and  name 
should  be  placed  in  the  border,  as  in  preceding  plates.  To 
letter  the  words  “ Problem  1,”  “Problem  2,”  etc.,  draw  horizontal 
lines  i inch  above  the  horizontal  center  line  and  the  lower  border 
line.  Draw  another  line  -j3g  inch  above,  to  limit  the  height  of  the 
P,  b and  l.  Draw  a third  line  inch  above  the  lower  line  as  a 
guide  line  for  the  tops  of  the  small  letters. 

Inking.  In  inking  PLATE  IV the  figures  should  be  inked 
first.  The  line  A C of  Problem  1 should  be  a full  line  as  it  is 
the  given  line;  the  arcs  and  line  D E,  being  construction  lines 
should  be  dotted.  In  Problem  2,  the  sides  of  the  angles  should 
be  full  lines.  Make  the  chord  L M and  the  arcs  dotted,  since 
as  before,  they  are  construction  lines. 

In  Problem  3,  the  line  A C is  the  given  line  and  P O is  the 
line  drawn  parallel  to  it.  As  E F and  the  arcs  do  not  form  a part 
of  the  problem  but  are  merely  construction  lines,  drawn  as  an  aid 
in  locating  P O,  they  should  be  dotted.  In  Problems  4,  5 and  6, 
the  assumed  lines  and  those  found  by  means  of  the  construction 
lines  should  be  full  lines.  The  arcs  and  construction  lines  should 
be  dotted.  In  Problem  6,  the  entire  circumference  need  not  be 
inked,  only  that  part  is  necessary  that  is  used  in  the  problem. 
The  inked  arc  should  however  be  of  sufficient  length  to  pass 
through  the  points  O,  P and  E. 

After  inking  the  figures,  the  border  lines  should  be  inked 
with  a heavy  line  as  before.  Also,  the  words  4 PLATE  IV"  and 
the  date  and  the  student’s  name.  Undereach  problem  the  words 
“Problem  1,”  “Problem  2,”  etc.,  should  be  inked;  lower  case  let- 
ters being  used  as  shown. 

PLATE  V. 

Pencilling.  In  laying  out  the  border  lines  and  centre  lines 
follow  the  directions  given  for  PLATE  IV  The  dot  and 
dash  lines  should  be  drawn  in  the  same  manner  as  there  are  to  be 
six  problems  on  this  plate. 


70 


PLATE 


MECHANICAL  DRAWING. 


21 


PROBLEM  7.  To  Draw  a Perpendicular  to  a Line  from  a 
Point  without  the  Line. 

Draw  the  horizontal  straight  line  A C about  3^  inches  long. 
Assume  the  point  P about  1L  inches  above  the  line.  With  P as 
a center  and  any  convenient  radius  (about  2 inches)  describe  an 
arc  cutting  A C at  E and  F.  The  radius  of  this  arc  must  always 
be  such  that  it  will  cut  A C in  two  points;  the  nearer  the  points 
E and  F are  to  A and  C,  the  greater  will  be  the  accuracy  of  the 
work.  Now  with  E and  F as  centers  and  any  convenient  radius 
(about  2i  inches)  draw  the  arcs  intersecting  below  A C at  T.  A 
line  through  the  points  P and  T will  be  perpendicular  to  A C. 

In  case  there  is  not  room  below  A C to  draw  the  arcs,  they 
may  be  drawn  intersecting  above  the  line  as  shown  at  N.  When- 
ever convenient,  draw  the  arcs  below  A C for  greater  accuracy. 

Proof.  Since  P and  T are  equally  distant  from  E and  F, 
the  line  P T is  perpendicular  to  A C. 

PROBLEM  8.  To  Bisect  a Given  Angle. 

First  Method.  When  the  sides  intersect. 

Draw  the  lines  O C and  O A forming  any  angle  (from  45  to 
60  degrees).  These  lines  should  be  about  8 inches  long.  With 
O as  a center  and  any  convenient  radius  (about  2 inches)  draw 
an  arc  intersecting  the  sides  of  the  angle  at  E and  F.  With  E 
and  F as  centers  and  a radius  of  lj  or  1|  inches,  describe  short 
arcs  intersecting  at  I.  A line  O D,  drawn  through  the  points  O 
and  I,  bisects  the  angle. 

In  solving  this  problem  the  arc  E F should  not  be  too  near 
the  vertex  if  accuracy  is  desired. 

Proof.  The  central  angles  A O D and  DOC  are  equal 
because  the  arc  E F is  bisected  by  the  line  O D.  The  point  I is 
equally  distant  from  E and  F. 

PROBLEM  9.  To  Bisect  a Given  Angle, 

Second  Method . When  the  lines  do  not  intersect. 

Draw  the  lines  A 0 and  E F about  4 inches  long  and  in  the 
positions  as  shown  on  PLATE  V Draw  A'  C'  and  E' F'  parallel 
to  A C and  E F and  at  such  equal  distances  from  them  that 
they  will  intersect  at  O.  Now  bisect  the  angle  C'  O F'  by 


73 


22 


MECHANICAL  DRAWING. 


the  method  of  Problem  8.  Draw  the  arc  G H and  with  G and  H 
as  centers  draw  the  arcs  intersecting  at  R.  The  line  O R bisects 
the  angle. 

Proof.  Since  A'  C'  is  parallel  to  A C and  E'  F'  parallel  to 
E F,  the  angle  C'  O F'  is  equal  to  the  angle  formed  by  the  lines 
A C and  E F.  Hence  as  O R bisects  angle  C'  O F'  it  also  bisects 
the  angle  formed  by  the  lines  A C and  E F. 

PROBLEM  10.  To  Divide  a Given  Line  into  any  Number 
of  Equal  Parts. 

Let  A C,  about  3-J  inches  long,  be  the  given  line.  Let  us 
divide  it  into  7 equal  parts.  Draw  the  line  A J at  least  4 inches 
long,  forming  any  convenient  angle  with  A C.  On  A J lay  off, 
by  means  of  the  dividers  or  scale,  points  D,  E,  F,  G,  etc.,  each  i inch 
apart.  If  dividers  are  used  the  spaces  need  not  be  exactly  1 
inch.  Draw  the  line  J C and  through  the  points  D,  E,  F,  G,  etc., 
draw  lines  parallel  to  J C.  These  parallels  will  divide  the  line 
A C into  7 equal  parts. 

Proof.  If  a series  of  parallel  lines,  cutting  two  straight 
lines,  intercept  equal  distances  on  one  of  these  lines,  they  also 
intercept  equal  distances  on  the  other. 

PROBLEM  11.  To  Construct  a Triangle  having  given  the 
Three  Sides. 

Draw  the  three  sides  as  follows : 

A C,  2|  inches  long. 

E F,  1L|-  inches  long. 

M N,  2^  inches  long. 

Draw  R S equal  in  length  to  A C.  With  R as  a center  and 
a radius  equal  to  E F describe  an  arc.  With  S as  a center  and 
a radius  equal  to  M N draw  an  arc  cutting  the  arc  previously 
drawn,  at  T.  Connect  T with  R and  S to  form  the  triangle. 

PROBLEM  12.  To  Construct  a Triangle  having  given 
One  Side  and  the  Two  Adjacent  Angles. 

Draw  the  line  M N 3^  inches  long  and  draw  two  angles 
A O D and  E F G.  Make  the  angle  A O D about  30  degrees  and 
E F G about  60  degrees. 

Draw  R S equal  in  length  to  M N and  at  R construct  an 


74 


MECHANICAL  DRAWING. 


23 


angle  equal  to  A O D.  At  S construct  an  angle  equal  to  E F G 
by  the  method  used  in  Problem  2.  PLATE  V shows  the  neces- 
sary arcs.  Produce  the  sides  of  the  angles  thus  constructed 
until  they  meet  at  T.  The  triangle  R T S will  be'  the  required 
triangle. 

After  drawing  these  six  figures  in  pencil,  draw  the  pencil 
lines  for  the  lettering.  The  lines  for  the  words  “ PLATE  V” 
date  and  name,  should  be  pencilled  as  explained  on  page  20. 
The  words  “ Problem  7,”  “ Problem  8,”  etc.,  are  lettered  as  for 
PLATE  IV. 

Inking.  In  inking  PLATE  V the  same  principles  should 
be  followed  as  stated  with  PLATE  IV.  The  student  should 
apply  these  principles  and  not  make  certain  lines  dotted  just 
because  they  are  shown  dotted  in  PLATE  V. 

After  inking  the  figures,  the  border  lines  should  be  inked 
and  the  lettering  inked  as  already  explained  in  connection  with 
previous  plates. 

PLATE  VI. 

Pencilling.  Lay  out  this  plate  in  the  same  manner  as  the 
two  preceding  plates. 

PROBLEM  13.  To  describe  an  Arc  or  Circumference 
through  Three  Given  Points  not  in  the  same  straight  line. 

Locate  the  three  points  A,  B and  C.  Let  the  distance 
between  A and  B be  about  2 inches  and  the  distance  between  A 
and  C be  about  2|  inches.  Connect  A and  B and  A and  C. 
Erect  perpendiculars  to  the  middle  points  of  A B and  A C.  This 
may  be  done  as  explained  with  Problem  1.  With  A and  B as 
centers  and  a radius  of  about  1|  inches,  describe  the  arcs  inter- 
secting at  I and  J.  With  A and  C as  centers  and  with  a radius 
of  about  1J  inches  draw  the  arcs,  intersecting  at  E and  F.  Now 
draw  light  pencil  lines  connecting  the  intersections  I and  J and 
E and  F.  These  lines  will  intersect  at  O. 

With  O as  a center  and  a radius  equal  to  the  distance  O A, 
describe  the  circumference  passing  through  A,  B and  C. 

Proof.  The  point  O is  equally  distant  from  A,  B and  C, 
since  it  lies  in  the  perpendiculars  to  the  middle  points  of  A B and 


75 


24 


MECHANICAL  DRAWING 


A C.  Hence  the  circumference  will  pass  through  A,  B and  C. 

PROBLEM  14.  To  inscribe  a Circle  in  a given  Triangle. 

Draw  the  triangle  L M N of  any  convenient  size.  M N may 
be  made  3f  inches,  L M,  2f  inches,  and  L N,  31  inches.  Bisect 
the  angles  M L N and  L M N.  The  bisectors  MI  and  L J may 
be  drawn  by  the  method  used  in  Problem  8.  Describe  the  arcs 
A C and  E F,  having  centers  at  L and  M respectively.  The  arcs 
intersecting  at  I and  J are  drawn  as  already  explained.  The 
bisectors  of  the  angles  intersect  at  O,  which  is  the  center  of  the 
inscribed  circle.  The  radius  of  the  circle  is  equal  to  the  perpen- 
dicular distance  from  O to  one  of  the  sides. 

Proof.  The  point  of  intersection  of  • the  bisectors  of  the 
angles  of  a triangle  is  equally  distant  from  the  sides. 

PROBLEM  15.  To  inscribe  a Regular  Pentagon  in  a given 
Circle. 

With  O as  a center  and  a radius  of  about  It  inches,  describe 
the  given  circle.  With  the  T square  and  triangles  draw  the  cen- 
ter lines  A C and  E F.  These  lines  should  be  perpendicular  to 
each  other  and  pass  through  O.  Bisect  one  of  the  radii,  such  as 
O C,  and  with  this  point  H as  a center  and  a radius  H E,  describe 
the  arc  E P.  This  arc  cuts  the  diameter  A C at  P.  With  E as 
a center  and  a radius  E P,  draw  arcs  cutting  the  circumference 
at  L and  Q.  With  the  same  radius  and  a center  at  L,  draw  the 
arc,  cutting  the  circumference  at  M.  To  find  the  point  N,  use 
either  M or  Q as  a center  and  the  distance  E P as  a radius. 

The  pentagon  is  completed  by  drawing  the  chords  E L,  L M, 
MN,NQ  and  Q E. 

PROBLEM  16.  To  inscribe  a Regular  Hexagon  in  a given 
Circle. 

With  O as  a center  and  a radius  of  If  inches  draw  the  given 
circle.  With  the  T square  draw  the  diameter  A D.  With  D as 
a center,  and  a radius  equal  to  O D,  describe  arcs  cutting  the 
circumference  at  C and  E.  Now  with  C and  E as  centers  and 
the  same  radius,  draw  the  arcs,  cutting  the  circumference  at  B 
and  F.  Draw  the  hexagon  by  joining  the  points  thus  formed. 

To  inscribe  a regular  hexagon  in  a circle  mark  off  chords 
equal  in  length  to  the  radius. 


76 


F’LsA  TE 


MECHANICAL  DRAWING, 


25 


To  inscribe  an  equilateral  triangle  in  a circle  the  same  method 
may  be  used.  The  triangle  is  formed  by  joining  the  opposite 
vertices  of  the  hexagon. 

Proof.  The  triangle  O C I)  is  an  equilateral  triangle  by 
construction.  Then  the  angle  C O D is  one-third  of  two  right 
angles  and  one-sixth  of  four  right  angles.  Hence  arc  C D is  one- 
sixth  of  the  circumference  and.  the  chord  is  a side  of  a regular 
hexagon. 

PROBLEM  17.  To  draw  a line  Tangent  to  a Circle  at  a 
given  point  on  the  circumference. 

With  O as  a center  and  a radius  of  about  1^  inches  draw 
the  given  circle.  Assume  some  point  P on  the  circumference 
Join  the  point  P with  the  center  O and  through  P draw  a line 
F P perpendicular  to  P O.  This  may  be  done  in  any  one  of  several 
methods.  Since  P is  the-  extremity  of  O P the  method  given  in 
Problem  6 of  PLATE  IV ] may  be  used. 

Produce  P O to  Q.  With  any  center  C,  and  a radius  C P 
draw  an  arc  or  circumference  passing  through  P.  Draw  E F a 
diameter  of  the  circle  whose  center  is  C and  through  F and  P 
draw  the  tangent. 

Proof.  A line  perpendicular  to  a radius  at  its  extremity  is 
tangent  to  the  circle. 

PROBLEM  18.  To  draw  a line  Tangent  to  a Circle  from  a 
point  outside  the  circle. 

With  O as  a center  and  a radius  of  about  1 inch  draw  the 
given  circle.  Assume  P some  point  outside  of  the  circle  about 
21-  inches  from  the  center  of  the  circle.  Draw  a straight  line 
passing  through  P and  O.  Bisect  P O and  with  the  middle 
point  F as  a center  describe  the  circle  passing  through  P and  O. 
Draw  a line  through  P and  the  intersection  of  the  two  circum- 
ferences C.  The  line  P C is  tangent  to  the  given  circle.  Simi- 
larly P E is  tangent  to  the  circle. 

Proof.  The  angle  P C O is  inscribed  in  a semi-circle  and 
hence  is  a right  angle.  Since  P C O is  a right  angle  P C is  per- 
pendicular to  C O.  The  perpendicular  to  a radius  at  its  extremity 
is  tangent  to  the  circumference. 

Inking.  In  inking  PLATE  VI  the  same  method  should  be 


79 


26 


MECHANICAL  DRAWING. 


followed  as  in  previous  plates.  The  name  and  address  should  be 
lettered  in  inclined  Gothic  capitals  as  before. 

PLATE  VII. 

Pencilling.  PLATE  VII should  be  laid  out  in  the  same 
manner  as  previous  plates.  Six  problems  on  the  ellipse,  spiral, 
parabola  and  hyperbola  are  to  be  constructed  in  the  six  spaces. 

PROBLEM  19.  To  draw  an  Ellipse  when  the  Axes  are 
given. 

Draw  the  lines  L M and  C D about  3|  and  2i  inches  long 
respectively.  Let  C D be  perpendicular  to  M N at  its  middle 
point  P.  Make  C P — P D.  These  two  lines  are  the  axes.  With 
C as  a center  and  a radius  equal  to  one-half  the  major  axis  or 
equal  to  L P,  draw  the  arc,  cutting  the  major  axis  at  E and  F. 
These  two  points  are  the  foci.  Now  mark  off  any  convenient 
distances  on  P M,  such  as  A,  B and  G. 

With  E as  a center  and  a radius  equal  to  L A,  draw  arcs 
above  and  below  L M.  With  F as  a center,  and  a radius  equal 
to  A M describe  short  arcs  cutting  those  already  drawn  as  shown 
at  N.  With  E as  a center  and  a radius  equal  to  L B draw  arcs 
above  and  below  L M as  before.  With  F as  a center  and  a radius 
equal  to  B M,  draw  arcs  intersecting  those  already  drawn  as  shown 
at  O.  The  point  P and  others  are  found  by  repeating  the  process. 
The  student  is  advised  to  find  at  least  12  points  on  the  curve  — 
6 above  and  6 below  L M.  These  12  points  with  L,  C,  M and 
D will  enable  the  student  to  draw  the  curve. 

After  locating  these  points,  a free  hand  curve  passing  through 
them  should  be  sketched. 

PROBLEM  20.  To  draw  an  Ellipse  when  the  two  Axes  are 
given. 

Second  Method.  Draw  the  two  axes  A B and  P Q in  the 
same  manner  as  for  Problem  19.  With  O as  a center  and  a radius 
equal  to  one-half  the  major  axis,  describe  the  circumference  A C 
D PI  F B.  Similarly  with  the  same  center  and  a radius  equal  to 
one-half  the  minor  axis,  describe  a circle.  Draw  any  radii  such 
as  O C,  O D,  O E,  O F,  etc.,  cutting  both  circumferences.  These 
radii  may  be  drawn  with  the  60  and  45  degree  triangles.  At  the 


80 


MECHANICAL  DRAWING. 


*27 


points  of  intersection  of  the  radii  with  the  large  circle  C D E and 
F,  draw  vertical  lines  and  from  the  intersection  of  the  radii  with 
the  small  circle  C',  D',  E',  and  F(  draw  horizontal  lines  intersect- 
ing the  vertical  lines.  The  intersections  of  these  lines  are  points 
on  the  curve. 

• As  in  Problem  19,  a free  hand  curve  should  be  sketched  pass- 
ing through  these  points.  About  five  points  in  each  quadrant 
will  be  sufficient. 

PROBLEM  21.  To  draw  an  Ellipse  by  means  of  a 
Trammel. 

As  in  the  two  preceding  problems,  draw  the  major  and  minor 
axes,  U Y and  X Y.  Take  a slip  of  paper  having  a straight 
edge  and  mark  off  C B equal  to  one-half  the  major  axis,  and  D B 
one-half  the  minor  axis.  Place  the  slip  of  paper  in  various 
positions  keeping  the  point  D on  the  major  axis  and  the  point  C 
on  the  minor  axis.  If  this  is  done  the  point  B will  mark  various 
points  on  the  curve.  Find  as  many  points  as  necessary  and  sketch 
the  curve. 

PROBLEM  22.  To  draw  a Spiral  of  one  turn  in  a circle. 

Draw  a circle  with  the  center  at  O and  a radius  of  11  inches. 
Mark  off  on  the  radius  O A,  distances  of  one-eighth  inch.  As 
O A is  1|  inches  long  there  will  be  1 2 of  these  distances.  Draw 
circles  through  these  points.  Now  draw  radii  O B,  O C,  O D 
etc.  each  30  degrees  apart  (use  the  30  degree  triangle).  This 
will  divide  the  circle  into  12  equal  parts.  The  curve  starts  at  the 
center  O.  The  next  point  is  the  intersection  of  the  line  O B and 
the  first  circle.  The  third  point  is  the  intersection  of  O C and 
the  second  circle.  The  fourth  point  is  the  intersection  of  O D 
and  the  third  circle.  Other  points  are  found  in  the  same  way. 
Sketch  in  pencil  the  curve  passing  through  these  points. 

PROBLEM  23.  To  draw  a Parabola  when  the  Abscissa  and 
Ordinate  are  given. 

Draw  the  straight  line  A B about  three  inches  long.  This 
line  is  the  axis  or  as  it  is  sometimes  called  the  abscissa.  At  A 
and  B draw  lines  perpendicular  to  A B.  Also  with  the  T square 
draw  E C and  F D,  11  inches  above  and  below  A B.  Let  A be 


83 


28 


MECHANICAL  DRAWING. 


the  vertex  of  the  parabola.  Divide  A E into  any  number  of 
equal  parts  and  divide  E C into  the  same  number  of  equal  parts. 
Through  the  points  of  division,  It,  S,  T,  U and  V,  draw  horizontal 
lines  and  connect  L,  M,  N,  O and  P,  with  A.  The  intersections 
of  the  horizontal  lines  with  the  oblique  lines  are  points  on  the 
curve.  For  instance,  the  intersection  of  A L and  the  line  V is 
one  point  and  the  intersection  of  A M and  the  liue  U is  another. 

The  lower  part  of  the  curve  A D is  drawn  in  the  same 
manner. 

PROBLEM  24.  To  draw  a Hyperbola  when  the  abscissa 
E X,  the  ordinate  A E and  the  diameter  X Y are  given. 

Draw  E F about  3 inches  long  and  mark  the  point  X,  1 inch 
from  E and  the  point  Y,  1 inch  from  X,  With  the  triangle  and 
T square,  draw  the  rectangles  A B D C and  O P Q R such  that 
A B is  1 inch  in  length  and  A C,  3 inches  in  length.  Divide 
A E into  any  number  of  equal  parts  and  A B into  the  same  num- 
ber of  equal  parts.  Draw  L X,  M X and  N X;  also  connect  T, 
U and  V with  Y.  The  first  point  on  the  curve  is  the  intersection 
A ; the  next  is  the  intersection  of  T Y and  L X ; the  third  the 
intersection  of  U Y and  M X.  The  remaining  points  are  found 
in  the  same  manner.  The  curve  X C and  the  right-hand  curve 
P Y Q are  found  by  repeating  the  process. 

Inking.  In  inking  the  figures  on  this  plate,  use  the  French 
or  irregular  curve  and  make  full  lines  for  the  curves  and  their 
axes.  The  construction  lines  should  be  dotted.  Ink  in  all  the 
construction  lines  used  in  finding  one-half  of  a curve,  and  in 
Problems  19,  20,  23  and  24  leave  all  construction  lines  in  pencil 
except  those  inked.  In  Problems  21  and  22  erase  all  construction 
lines  not  inked.  The  trammel  used  in  Problem  21  may  be  drawn 
in  the  position  as  shown,  or  it  may  be  drawn  outside  of  the  ellipse 
in  any  convenient  place. 

The  same  lettering  should  be  done  on  this  plate  as  on  previous 
plates. 

PLATE  VIII. 

Pencilling.  In  laying  out  Plate  VIII,  draw  the  border  lines; 
and  horizontal  and  vertical  center  lines  as  in  previous  plates,  to 
divide  the  plate  into  four  spaces  for  the  four  problems. 


84 


AP.  /0O/.  /-/£r/=?&£7/=?T  £?/S^A/JJl-  £T/=?  C‘/~//C'yA GO.  //LZ_. 


MECHANICAL  DRAWING. 


29 


PROBLEM  25.  To  construct  a Cycloid  when  the  diameter 
of  the  generating  circle  is  given. 

With  0'  as  a center  and  a radius  of  inch  draw  a circle,  and 
tangent  to  it  draw  the  indefinite  horizontal  straight  line  A B. 
Divide  the  circle  into  any  number  of  equal  parts  (12  for  instance) 
and  through  these  points  of  division  C,  D,  E,  F,  etc.,  draw  hori- 
zontal lines.  Now  with  the  dividers  set  so  that  the  distance 
between  the  points  is  equal  to  the  chord  of  the  arc  C D,  mark  off 
the  points  L,  M,  N,  O,  P on  the  line  *A  B,  commencing  at  the 
point  H.  At  these  points  erect  perpendiculars  to  the  center  line 
G O'.  This  center  line  is  drawn  through  the  point  O'  with  the 
T square  and  is  the  line  of  centers  of  the  generating  circle  as  it 
rolls  along  the  line  A B.  Now  with  the  intersections  Q,  R,  S, 
T,  etc.,  of  these  verticals  with  the  center  line  as  centers  describe 
arcs  of  circles  as  shown.  The  points  on  the  curve  are  the  inter- 
sections of  these  arcs  and  the  horizontal  lines  drawn  through  the 
points  C,  D,  E,  F,  etc.  Thus  the  intersection  of  the  arc  whose 
center  is  Q and  the  horizontal  line  through  C is  a point  I on  the 
curve.  Similarly,  the  intersection  of  the  arc  whose  center  is  R 
and  the  horizontal  line  through  D is  another  point  J on  the  curve. 
The  remaining  points,  as  well  as  those  on  the  right-hand  side,  are 
found  in  the  same  manner.  To  obtain  great  accuracy  in  this 
curve,  the  circle  should  be  divided  into  a large  number  of  equal 
parts,  because  the  greater  the  number  of  divisions  the  less  the  error 
due  to  the  difference  in  length  of  a chord  and  its  arc. 

PROBLEM  26.  To  construct  an  Epicycloid  when  the  di= 
ameter  of  the  generating  circle  and  the  diameter  of  the  director 
circle  are  given. 

The  epicycloid  and  hypocycloid  may  be  drawn  in  the  same 
manner  as  the  cycloid  if  arcs  of  circles  are  used  in  place  of  the 
horizontal  lines.  With  O as  a center  and  a radius  of  | inch 
describe  a circle.  Draw  the  diameter  E F of  this  circle  and  pro- 
duce E F to  G such  that  the  line  F G is  2|^  inches  long.  With 
G as  a center  and  a radius  of  2^  inches  describe  the  arc  A B of 
the  director  circle.  With  the  same  center  G,  draw  the  arc  P Q 
which  will  be  the  path  of  the  center  of  the  generating  circle  as  it 
rolls  along  the  arc  A B.  Now  divide  the  generating  circle  into 


87 


30 


MECHANICAL  DRAWING. 


any  number  of  equal  parts  (twelve  for  instance)  and  through  the 
points  of  division  H,  I,  L,  M,  and  N,  draw  arcs  having  G as  a 
center.  With  the  dividers  set  so  that  the  distance  between  the 
points  is  equal  to  the  chord  H I,  mark  off  distances  on  the 
director  circle  A F B.  Through  these  points  of  division  R,  S, 
T,  U,  etc.,  draw  radii  intersecting  the  arc  P Q in  the  points  IT,  S', 
T',  etc.,  and  with  these  points  as  centers  describe  arcs  of  circles 
as  in  Problem  25.  The  intersections  of  these  arcs  with  the  arcs 
already  drawn  through  the  points  H,  I,  L,  M,  etc.,  are  points  on 
the  curve.  Thus  the  intersection  of  the  circle  whose  center  is  IT 
with  the  arc  drawn  through  the  point  H is  a point  upon  the  curve. 
Also  the  arc  whose  center  is  S'  with  the  arc  drawn  through  the 
point  I is  another  point  on  the  curve.  The  remaining  points  are 
found  by  repeating  this  process. 

PROBLEM  27.  To  draw  an  Hypocydoid  when  the  diam= 
eter  of  the  generating  circle  and  the  radius  of  the  director  circle 
are  given. 

With  O as  a center  and  a radius  of  4 inches  describe  the  arc 
E F,  which  is  the  arc  of  the  director  circle.  Now  witli  the  same 
center  and  a Radius  of  3-^  inches,  describe  the  arc  A B,  which  is  the 
line  of  centers  of  the  generating  circle  as  it  rolls  on  the  director 
circle.  With  O'  as  a center  and  a radius  of  | inch  describe  the 
generating  circle.  As  before,  divide  the  generating  circle  into 
any  number  of  equal  parts  (12  for  instance)  and  with  these  points 
of  division  L,  M,  N,  O,  etc.,  draw  arcs  having  O as  a center. 
Upon  the  arc  E F,  lay  off  distances  Q R,  R S,  S T,  etc.,  equal  to 
the  chord  Q L.  Draw  radii  from  the  points  R,  S,  T,  etc.,  to  the 
center  of  the  director  circle  O and  describe  arcs  of  circles  having  a 
radius  equal  to  the  radius  of  the  generating  circle,  using  the 
points  G,  I,  J,  etc.,  as  centers.  As  in  Problem  26,  the  inter- 
sections of  the  arcs  are  the  points  on  the  curve.  By  repeating 
this  process,  the  right-hand  portion  of  the  curve  may  be  drawn. 

PROBLEM  28.  To  draw  the  Involute  of  a circle  when  the 
diameter  of  the  base  circle  is  known. 

With  point  O as  a center  and  a radius  of  1 inch,  describe  the 
base  circle.  Now  divide  the  circle  into  any  number  of  equal  parts 
16  for  instance)  and  connect  the  points  of  division  with  the  cen* 


88 


MECHANICAL  DRAWING. 


31 


ter  of  the  circle  by  drawing  the  radii  0 C,  O D,  O E,  O F,  etc., 
to  O B.  At  the  point  D,  draw  a light  pencil  line  perpendicular 
to  the  radius  O D.  This  line  will  be  tangent  to  the  circle. 
Similarly  at  the  points  E,  F,  G,  H,  etc.,  draw  tangents  to  the 
circle.  Now  set  the  dividers  so  that  the  distance  between  the 
points  will  be  equal  to  the  chord  of  the  arc  C D,  and  measure  this 
distance  from  D along  the  tangent.  Beginning  with  the  point  E, 
measure  on  the  tangent  a distance  equal  to  two  of  these  chords, 
from  the  point  F measure  on  the  tangent  three  divisions,  and  from 
the  point  G measure  a distance  equal  to  four  divisions  on  the 
tangent  G P.  Similarly,  measure  distances  on  the  remaining 
tangents,  each  time  adding  the  length  of  the  chord.  This  will 
give  the  points  Q,  R,  S and  T.  Now  sketch  a light  pencil  line 
through  the  points  L,  M,  N,  P,  etc.,  to  T.  This  curve  will  be  the 
involute  of  the  circle. 

Inking.  The  same  rules  are  to  be  observed  in  inking  PLATE 
VIII  as  were  followed  in  the  previous  plates,  that  is,  the  curves 
should  be  inked  in  a full  line,  using  the  French  or  irregular  curve. 
All  arcs  and  lines  used  in  locating  the  points  on  one-half  of  the 
curve  should  be  inked  in  dotted  lines.  The  arcs  and  lines  used  in 
locating  the  points  of  the  other  half  of  the  curve  may  be  left  in 
pencil  in  Problems  25  and  26.  In  Problem  28,  all  construction 
lines  should  be  inked.  After  completing  the  problems  the  same 
lettering  should  be  done  on  this  plate  as  on  previous  plates. 


89 


PIERCED- 


11011  THREE-COARTER-OCALE-DETAIL'OF'CUT  -3TONE -WORK- 

CENTRAL  PAVILION  ■ EASTERN-  PARKWAY-  ELEVATION- 


BROOKLYN.'*  INSTITUTE.*  k?kim*hlad*an°*whitc  *a£ckt:5- 


i 

DRAWING  h<?213 

3E.PT  Z VJ3WA e T WOU7 


REPRODUCTION  OF  A TYPICAL  ARCHITECTURAL  DRAWING  FROM  ONE  OF  THE  FOREMOST  AMERICAN  OFFICES. 
Note  how  much  information  is  crowded  into  a single  sheet. 


MECHANICAL  DRAWING. 

PART  III. 


PROJECTIONS. 


ORTHOGRAPHIC  PROJECTION. 

Orthographic  Projection  is  the  art  of  representing  objects  of 
three  dimensions  by  views  on  two  planes  at  right  angles  to  each 
other,  in  such  a way  that  the  forms  and  positions  may  be  completely 
determined.  The  two  planes  are  called  planes  of  projection  or 
co-ordinate  planes,  one  being  vertical  and  the  other  horizontal,  as 
shown  in  Fig.  1.  These  planes  are  sometimes  designated  V and  H 
respectively.  The  intersection  of  V and  H is  known  as  the  ground 
line  G L. 

The  view  or  projection  of  the  figure  on  the  plane  gives  the 
same  appearance  to  the  eye  placed  in  a certain  position  that  the 
object  itself  does.  This  position 
of  the  eye  is  at  an  infinite  dist- 
ance from  the  plane  so  that  the 
rays  from  it  to  points  of  a limited 
object  are  all  perpendicular  to  the 
plane.  Evidently  then  the  view  of 
a point  of  the  object  is  on  the  plane 
6 and  in  the  ray  through  the  point 

and  the  eye  or  where  this  perpendicular  to  the  plane  pierces  it. 

Let  a , Fig.  1,  be  a point  in  space,  draw  a perpendicular  from  a 
to  V.  Where  this  line  strikes  the  vertical  plane,  the  projection  of  a 
is  found,  namely  at  ay.  Then  drop  a perpendicular  from  a to  the 
horizontal  plane  striking  it  at  ah,  which  is  the  horizontal  projection 
of  the  point.  Drop  a perpendicular  from  av  to  H;  this  will 
intersect  G L at  o and  be  parallel  and  equal  to  the  line  a ah.  In 
the  same  way  draw  a perpendicular  from  ah  to  V,  this  also  will 
intersect  G L at  o and  will  be  parallel  and  equal  to  a av.  In  other 
words,  the  perpendicular  to  G L from  the  projection  of  a point  on 
either  plane  equals  the  distance  of  the  point  from  the  other  plane. 
B in  Fig.  1,  shows  a line  in  space.  Bv  is  its  V projection,  and  Bb 


91 


4 


MECHANICAL  DRAWING 


its  H projection,  these  being  determined  by  finding  views  of  points 
at  its  ends  and  connecting  the  points. 

Instead  of  horizontal  projection  and  vertical  projection,  the 
terms  plan  and  elevation  are  commonly  used. 

Suppose  a cube,  .one  inch  on  a side,  to  be  placed  as  in  Fig.  2, 
with  the  top  face  horizontal  and  the  front  face  parallel  to  the 
vertical  plane.  Then  the  plan  will  be  a one-inch  square,  and  the 
elevation  also  a one-inch  square.  In  general  the  plan  is  a repre- 
sentation of  the  top  of  the  object,  and  the  elevation  a view  of  the 
front.  The  plan  then  is  a top  view,  and  the  elevation  a front  view. 


Fig.  3. 


Thus  far  the  two  planes  have  been  represented  at  right  angles 
to  each  other,  as  they  are  in  space.  In  order  that  they  may  be 
shown  more  simply  and  on  the  one  plane  of  the  paper,  H is 
revolved  about  G L as  an  axis  until  it  lies  in  the  same  plane  as  V 
as  shown  in  Fig.  2.  The  lines  lh  O and  2h  N,  being  perpendicular 
to  G L,  are  in  the  same  straight  line  as  5V  O and  6V  N,  which  also 
are  perpendicular  to  G L.  That  is — two  views  of  a point  are 
always  in  a line  perpendicular  to  G L.  From  this  it  is  evident 
that  the  plan  must  be  vertically  below  the  elevation,  point  for  point. 
Now  looking  directly  at  the  two  planes  in  the  revolved  position,  we 


92 


MECHANICAL  DRAWING 


5 


get  a true  orthographic  projection  of  the  cube  as  shown  in  Fig.  3. 

All  points  on  an  object  at  the  same  height  must  appear  in 
elevation  at  the  same  distance  above  the  ground  line.  If  numbers 
1,  2,  3,  and  4 on  the  plan,  Fig.  3,  indicate  the  top  corners  of  the 
cube,  then  these  four  points,  being  at  the  same  height,  must  be 


4v  Qv 

shown  in  elevation  at  the  same  height  and  at  the  top. , and  - - 

i lv  2V  • 


The  top  of  the  cube,  1,  2, 3, 4,  is  shown  in  elevation  as  the  straight  line 
4V  3V 

-g-  ■ This  illustrates  the  fact  that  if  a surface  is  perpendicular 


to  either  plane  or  projection,  its  projection  on  that  plane  is  simply 
a line;  a straight  line  if  the  surface  is  plane,  a curved  line  if  the 
surface  is  curved.  From  the  same  figure  it  is  seen  that  the  top 
edge  of  the  cube,  1 4,  has  for  its  projection  on  the  vertical  plane 


Fig.  4. 


straigni  line  is  perpendicular  to  either  V or  H,  its  projection  on 
that  plane  is  a point,  and  on  the  other  plane  is  a line  equal  in 
length  to  the  line  itself,  and  perpendicular  to  the  ground  line. 

Fig.  4 is  given  as  an  exercise  to  help  to  show  clearly  the  idea 
of  plan  and  elevation. 

A = a point  B"  above  H,  and  A"  in  front  of  V. 

B = square  prism  resting  on  H,  two  of  its  faces  parallel  to  V, 

C = circular  disc  in  space  parallel  to  V. 

D = triangular  card  in  space  parallel  to  V. 

E = cone  resting  on  its  base  on  H. 

F = cylinder  perpendicular  to  V,  and  with  one  end  resting  against  V. 

G = line  perpendicular  to  H. 

H = triangular  pyramid  above  H,  with  its  base  resting  against  V. 


93 


6 


MECHANICAL  DRAWING. 


Suppose  in  Fig.  5,  that  it  is  desired  to  construct  the  pro- 
jections of  a prism  li  in.  square,  and  2 in.  long,  standing  on  one 
end  on  the  horizontal  plane,  two  of  its  faces  being  parallel  to  the 
vertical  plane.  In  the  first  place,  as  the  top  end  of  the  prism  is  a 
square,  the  top  view  or  plan  will  be  a square  of  the  same  size, 
that  is,  11-  in.  Then  since  the  prism  is  placed  parallel  to  and  in 
front  of  the  vertical  plane  the  plan,  11  in.  square,  will  have  two 
edges  parallel  to  the  ground  line.  As  the  front  face  of  the  prism 


ELEVA7  ION 
OR 

FRONT  VIEW 




'2 

PLAN 

OR 

TOP  VIEW 


Fig.  5. 


is  parallel  to  the  vertical  plane  its  projection  on  V wifi  be  a rect> 
angle,  equal  in  length  and  width  to  the  length  and  width  respec- 
tively of  the  prism,  and  as  the  prism  stands  with  its  base  on  H, 
the  elevation,  showing  height  above  H,  must  have  its  base  on  the 
ground  line.  Observe  carefully  that  points  in  elevation  are  verti- 
cally over  corresponding  points  in  plan. 

The  second  drawing  in  Fig.  5 represents  a prism  of  the  same 
size  lying  on  one  side  on  the  horizontal  plane,  and  with  the  ends 
parallel  to  V. 

The  principles  which  have  been  used  thus  far  may  be  stated 
as  follows,  — 


MECHANICAL  DRAWING. 


7 


1.  If  a line  or  point  is  on  either  plane,  its  other  projection 
must  be  in  the  ground  line. 

2.  Height  above  H is  shown  m elevation  as  height  above 
the  ground  line,  and  distance  in  front  of  the  vertical  plane  is  shown 
in  plan  as  distance  from  the  ground  line. 

3.  If  a line  is  parallel  to  either  plane,  its  actual  length  is 
shown  on  that  plane,  and  its  other  projection  is  parallel  to  the 
ground  line.  A line  oblique  to  either  plane  has  its  projection  on 
that  plane  shorter  than  the  line  itself,  and  its  other  projection 
oblique  to  the  ground  line.  No  projection  can  be  longer  than  the 
line  itself. 

4.  A plane  surface  if  parallel  to  either  plane,  is  shown  on 


Fig.  6.  Fig.  7. 


that  plane  in  its  true  size  and  shape ; if  oblique  it  is  shown 
smaller  than  the  true  size,  and  if  perpendicular  it  is  shown  as  a 
straight  line.  Lines  parallel  in  space  must  have  their  V projec- 
tions parallel  to  each  other  and  also  their  H projections. 

If  two  lines  intersect,  their  projections  must  cross,  since  tli9 
point  of  intersection  of  the.  lines  is  a point  on  both  lines,  and 
therefore  the  projections  of  this  point  must  be  on  the  projections 
of  both  lines,  or  at  their  intersection.  In  order  that  intersecting 
lines  may  be  represented,  the  vertical  projections  must  intersect 
in  a point  vertically  above  the  intersection  of  the  horizontal  pro- 


95 


8 


MECHANICAL  DRAWING. 


jections.  Thus  Fig.  6 represents  two  lines  which  do  intersect  as 
Cv  crosses  Dv  at  a point  vertically  above  the  intersection  of  Ch  and 
D71.  In  Fig.  7,  however,  the  lines  do  not  intersect  since  the  inter- 
sections of  their  projections  do  not  lie  in  the  same  vertical  line. 

In  Fig.  8 is  given  the  plan  and  elevation  of  a square  pyramid 
standing  on  the  horizontal  plane.  The  height  of  the  pyramid  is 
the  distance  A B.  The  slanting  edges  of  the  pyramid,  AC,  AD, 
etc.,  must  be  all  of  the  same  length,  since  A is  directly  above  the 

center  of  the  base.  What  this  length 
is,  however,  does  not  appear  in  either 
projection,  as  these  edges  are  not 
parallel  to  either  V or  H. 

Suppose  that  the  pyramid  be 
turned  around  into  the  dotted  posi- 
tion C,  Dj  E,  F(  where  the  horizontal 
projections  of  two  of  the  slanting 
edges,  A C,  and  A E,  are  parallel  to 
the  ground  line.  These  two  edges, 
having  their  horizontal  projections 
parallel  to  the  ground  line,  are  now 
parallel  to  V,  and  therefore  their  new 
vertical  projections  will  show  their 
true  lengths.  The  base  of  the  pyra- 
mid is  still  on  H,  and  therefore  is 
projected  on  V in  the  ground  line. 
The  apex  is  in  the  same  place  as  be- 
fore, hence  the  vertical  projection  of 
the  pyramid  in  its  new  position  is  shown  by  the  dotted  lines.  The 
vertical  projection  A C,v  is  the  true  length  of  edge  A C.  Now  if 
we  wish  to  find  simply  the  true  length  of  A C,  it  is  unnecessary  to 
turn  the  whole  pyramid  around,  as  the  one  line  A C will  be  sufficient. 

The  principle  of  finding  the  true  length  of  lines  is  this,  and 
can  be  applied  to  any  case  : Swing  one  projection  of  the  line  par- 
allel to  the  ground  line,  using  one  end  as  center.  On  the  other 
projection  the  moving  end  remains  at  the  same  distance  from  the 
ground  line,  and  of  course  vertically  above  or  below  the  same  end 
in  its  parallel  position.  This  new  projection  of  the  line  shows  its 
true  length.  See  the  three  Figures  at  the  top  of  page  9. 


96 


MECHANICAL  DRAWING. 


9 


Third  plane  of  projection  or  profile  plane.  A plane  perpen- 
dicular to  both  co-ordinate  planes,  and  hence  to  the  ground  line,  is 


called  a profile  plane . This  plane  is  vertical  in  position,  and  may 
be  used  as  a plane  of  projection.  A projection  on  the  profile  plane 
is  called  a profile  view,  or  end  view , or  sometimes  edge  view,  and 
is  often  required  in  machine  or  other  drawing  when  the  plan  and 
elevation  do  not  sufficiently  give  the  shape  and  dimensions. 

A projection  on  this  plane  is  found  in  the  same  way  as  on  the 


V plane,  that  is,  by  perpendiculars  drawn  from  points  on  the 
object. 

Since,  however,  the  profile  plane  is  perpendicular  to  the 
ground  line,  it  will  be  seen  from  the  front  and  top  simply  as  a 


97 


to 


MECHANICAL  DRAWING. 


straight  line ; in  order  that  the  size  and  shape  of  the  profile  view 
may  be  shown,  the  profile  plane  is  revolved  into  V using  its  inter- 
section  with  the  vertical  plane  as  the  axis. 

Given  in  Fig.  9,  the  line  A B by  its  two  projections  Av  Bw  and 
Ah  B71,  and  given  also  the  profile  plane.  Now  by  projecting  the 
line  on  the  profile  by  perpendiculars,  the  points  A*  B,v  and  B,71  A,71 
are  found.  Revolving  the  profile  plane  like  a door  on  its  hinges,  all 
points  in  the  plane  will  move  in  horizontal  circles,  so  the  horizontal 
projections  A,71  and  B/1  will  move  in  arcs  of  circles  with  O as  center 
to  the  ground  line,  and  the  vertical  projections  B,v  and  A,v  will  move 
in  lines  parallel  to  the  ground  line  to  positions  directly  above  the 
* revolved  points  in  the  ground  line,  giving  the  profile  view  of  the 
line  Ap  Bp.  Heights,  it  will  be  seen,  are  the  same  in  profile  view 

as  in  elevation.  By  referring  to 
the  rectangular  prism  in  the  same 
figure,  we  see  that  the  elevation 
gives  vertical  dimensions  and  those 
parallel  to  Y,  while  the  end  view 
shows  vertical  dimensions  and 
those  perpendicular  to  Y.  The 
profile  view  of  any  object  may  be 
found  as  shown  for  the  line  A B 
by  taking  one  point  at  a time. 

In  Fig.  10  there  is  repre- 
sented a rectangular  prism  or 
block,  whose  length  is  twice  the 
width.  The  elevation  shows  its 
height.  As  the  prism  is  placed  at 
an  angle,  three  of  the  vertical  edges  will  be  visible,  the  fourth 
one  being  invisible. 

In  mechanical  drawing  lines  or  edges  which  are  invisible  are 
drawn  dotted.  The  edges  which  in  projection  form  a part  of  the 
outline  or  contour  of  the  figure  must  always  be  visible,  hence 
always  full  lines.  The  plan  shows  what  lines  are  visible  in  eleva- 
tion, and  the  elevation  determines  what  are  visible  in  plan.  In 
Fig.  10,  the  plan  shows  that  the  dotted  edge  A B is  the  back  edge, 
and  in  Fig.  11,  the  dotted  edge  C D is  found,  by  looking  at  the 
elevation,  to  be  the  lower  edge  of  the  triangular  prism.  In  general, 


Fig.  10. 


98 


Mechanical  drawing. 


n 


if  in  elevation  an  edge  projected  ivithin  the  figure  is  a back  edge, 
it  must  be  dotted,  and  in  plan  if  an  edge  projected  within  the 
outline  is  a lower  edge  it  is  dotted. 

Fig.  12  is  a circular  cylinder  with  the  length  vertical  and 


Fig.  11. 


with  a hole  part  way  through  as  shown  in  elevation.  Fig.  IB  is 
plan,  elevation  and  end  view  of  a triangular  prism  with  a square 
hole  from  end  to  end.  The  plan  and  elevation  alone  would  be 
insufficient  to  determine  positively  the  shape  of  the  hole,  but  the 
end  view  shows  at  a glance  that  it  is  square. 

In  Fig.  14  is  shown  plan  and  elevation  of  the  frustum  of  a 
square  pyramid,  placed  with  its  base  on  the  horizontal  plane.  If  the 
frustum  is  turned  through  30°,  as  shown  in  the  plan  of  Fig.  15, 
the  top  view  or  plan  must  still  be  the  same  shape  and  size,  and  as 
the  frustum  has  not  been  raised  or  lowered,  the  heights  of  all 
points  must  appear  the  same  in  elevation  as  before  in  Fig.  14. 
The  elevation  is  easily  found  by  projecting  points  up  from  the 
plan,  and  projecting  the  height  of  the  top  horizontally  across  from 
the  first  elevation,  because  the  height  does  not  change. 

The  same  principle  is  further  illustrated  in  Figs.  16  and  17. 
The  elevation  of  Fig.  16  shows  a square  prism  resting  on  one  edge, 
and  raised  up  at  an  angle  of  30°  on  the  right-hand  side.  The 


99 


12 


MECHANICAL  DRAWING. 


plan  gives  the  width  or  thickness,  | in.  Notice  that  the  length  of 
the  plan  is  greater  than  2 in.  and  that  varying  the  angle  at 


Fig.  12.  Fig.  13. 


which  the  pri«m  is  slanted  would  change  the  length  of  the  plan. 
Now  if  the  prism  be  turned  around  through  any  angle  with  the 
vertical  plane,  the  lower  edge  still  being  on  H,  and  the  inclination 


Fig.  14.  Fig.  15. 

of  30°  with  II  remaining  the  same,  the  plan  must  remain  the  same 
size  and  shape. 

If  the  angle  through  which  the  prism  be  turned  is  45°,  we 


100 


MECHANICAL  DRAWING. 


13 


have  the  second  plan,  exactly  the  same  shape  and  size  as  the  first. 
The  elevation  is  found  by  projecting  the  corners  of  the  prism  ygv- 


Fig.  16. 


tically  up  to  the  heights  of  the  same  points  in  the  first  elevation. 
All  the  other  points  are  found  in  the  same  way  as  point  No.  1. 


Fig.  17. 


Three  positions  of  a rectangular  prism  are  shown  in  Fig.  17. 
In  the  first  view,  the  prism  stands  on  its  base,  its  axis  therefore 


101 


14 


MECHANICAL  DRAWINGS 


is  parallel  to  the  vertical  plane.  In  the  second  position,  the  axis  is 
still  parallel  to  V and  one  corner  of  the  base  is  on  the  horizontal 
plane.  The  prism  has  been  turned  as  if  on  the  line  l/l  ~iv  as  an 
axis,  so  that  the  inclination  of  all  the  faces  of  the  prism  to  the 
vertical  plane  remains  the  same  as  before.  That  is,  if  in  the  first 
figure  the  side  A B C D makes  an  angle  of  30°  with  the  vertical, 
the  same  side  in  the  second  position  still  makes  30°  with  the  ver- 


tical plane.  Hence  the  elevation  of  No.  2 is  the  same  shape  and  size 
as  in  the  first  case.  The  plan  is  found  by  projecting  the  corners 
down  from  the  elevation  to  meet  horizontal  lines  projected  across 
from  the  corresponding  points  in  the  first  plan.  The  third  posi- 
tion shows  the  prism  with  all  its  faces  and  edges  making  the  same 
angles  with  the  horizontal  as  in  the  second  position,  but  with  the 
plan  at  a different  angle  with  the  ground  line.  The  plan  then  is 
the  same  shape  and  size  as  in  No.  2,  and  the  elevation  is  found  by 
projecting  up  to  the  same  heights  as  shown  in  the  preceeding 
elevation.  This  principle  may  be  applied  to  any  solid,  whether 
bounded  by  plane  surfaces  or  curved. 

This  principle  as  far  as  it  relates  to  heights,  is  the  same  that 
was  used  for  profile  views.  An  end  view  is  sometimes  necessary 
before  the  plan  or  elevation  of  an  object  can  be  drawn.  Suppose 
that  in  Fig.  18  we  wish  to  draw  the  plan  and  elevation  of  a tri- 
angular prism  3"  long,  the  end  of  which  is  an  equilateral  triangle 


102 


MECHANICAL  DRAWING. 


15 


\y  on  each  side.  The  prism  is  lying  on  one  of  its  three  faces  on 
H,  and  inclined  toward  the  vertical  plane  at  an  angle  of  30°.  We 

are  able  to  draw  the  plan  at 
once,  because  the  width  will  be 
1^  inches,  and  the  top  edge  will 
be  projected  half  way  between 
the  other  two.  The  length  of 
the  prism  will  also  be  shown. 
Before  we  can  draw  the  elevation, 
we  must  find  the  height  of  the 
top  edge.  This  height,  however, 
must  be  equal  to  the  altitude  of 
the  triangle  forming  the  end  of 
the  prism.  All  that  is  necessary, 
then,  is  to  construct  an  equilat- 
eral triangle  on  each  side,  and  measure  its  altitude. 

A very  convenient  way  to  do  this  is  shown  in  the  figure  by 
laying  one  end  of  the  prism  down  on  H.  A similar  construction 
is  shown  in  Fig.  19,  but  with  one  face  of  the  prism  on  V instead 
of  on  H. 

In  all  the  work  thus  far  the  plan  has  been  drawn  below  and 
the  elevation  above.  This  order  is  sometimes  inverted  and  the 
plan  put  above  the  elevation,  but  the  plan  still  remains  a top  view 
no  matter  where  placed,  so  that  after  some  practice  it  makes  but 
little  difference  to  the  draughtsman  which  method  is  employed. 

SHADE  LINES. 

It  is  often  the  case  in  machine  drawing  that  certain  lines  or 
edges  are  made  heavier  than  others.  These  heavy  lines  are  called 
shade  lines,  and  are  used  to  improve  the  appearance  of  the  draw- 
ing, and  also  to  make  clearer  in  some  cases  the  shape  of  the 
object.  The  shade  lines  are  not  put  on  at  random,  but  according 
to  some  system.  Several  systems  are  in  use,  but  only  that  one 
which  seems  most  consistent  will  be  described.  The  shade  lines 
are  lines  or  edges  separating  light  faces  from  dark  ones,  assuming 
the  light  always  to  come  in  a direction  parallel  to  the  dotted 
diagonal  of  the  cube  shown  in  Fig.  20.  The  direction  of  the 
light,  then,  may  be  represented  on  H by  a line  at  45°  running 


103 


16 


MECHANICAL  DRAWING. 


backward  to  the  right  and  on  Y by  a 45°  line  sloping  downward 
and  to  the  right.  Considering  the  cube  in  Fig.  20,  if  the  light 
comes  in  the  direction  indicated,  it  is  evident  that  the  front,  left- 
hand  side  and  top  will  be  light,  and  the  bottom,  back  and  right- 
hand  side  dark.  On  the  plan,  then,  the  shade  lines  will  be  the 
back  edge  1 2 and  the  right-hand  edge  2 3,  because  these  edges 
are  between  light  faces  and  dark  ones.  On  the  elevation*  since 
the  front  is  light,  and  the  right-hand  side  and  bottom  dark,  the  edges 
3 T and  8 7 are  shaded.  As  the  direction  of  the  light  is  represented 
on  the  plan  by  45°  lines  and  on  the  elevation  also  by  45°  lines, 


Fig.  20. 

we  may  use  the  45°  triangle  with  the  T-square  to  determine 
the  light  and  dark  surfaces,  and  hence  the  shade  lines.  If 
the  object  stands  on  the  horizontal  plane,  the  45°-  triangle  is  used 
on  the  plan,  as  shown  in  Fig.  21,  but  if  the  length  is  perpen- 
dicular to  the  vertical  plane,  the  45°  triangle  is  used  on  the  eleva- 
tion, as  shown  in  Fig.  22.  This  is  another  way  of  saying  that  the 
45°  triangle  is  used  on  that  projection  of  the  object  which  shows 
the  end.  By  applying  the  triangle  in  this  way  we  determine  the 
light  and  dark  surfaces,  and  then  put  the  shade  lines  between 
them.  Dotted  lines,  however,  are  never  shaded,  so  if  a line 
which  is  between  a light  and  a dark  surface  is  invisible  it  is  not 


MECHANICAL  DRAWING. 


17 


shaded.  In  Fig.  21  the  plan  shows  the  end  of  the  solid,  hence  the 
45°  triangle  is  used  in  the  direction  indicated  by  the  arrows. 

This  shows  that  the  light  strikes  the  left-hand  face,  but  not 
the  back  or  the  right-hand.  The  top  is  known  to  be  light  with- 


out the  triangle,  as  the  light  comes  downward,  so  the  shade  edges 
on  the  plan  are  the  back  and  right-hand.  On  the  elevation  two 
faces  of  the  prism  are  visible ; one  is  light,  the  other  dark,  hence 
the  edge  between  is  shaded.  The  left-hand  edge,  being  between 
a light  face  and  a dark  one  is  a shade  line.  The  right-hand  face 
is  dark,  the  top  of  the  prism  is  light,  hence  the  upper  edge  of  this 
face  is  a shade  line.  The  right-hand  edge  is  not  shaded,  because 
by  referring  to  the  plan,  it  is  seen  to  be  between  two  dark 
surfaces.  In  shading  a cylinder  or  a cone  the  same  rule  is  fol- 
lowed, the  only  difference  being  that  as  the  surface  is  curved,  the 
light  is  tangent,  so  an  element  instead  of  an  edge  marks  the 
separation  of  the  dark  from  the  light,  and  is  not  shaded.  The 
elements  of  a cylinder  or  cone  should  never  be  shaded,  but  the 
bases  may.  In  Fig.  23,  Nos.  3 and  4,  the  student  should  carefully 
notice  the  difference  between  the  shading  of  the  cone  and  cylinder. 


105 


18 


MECHANICAL  DRAWING. 


If  in  No.  4 the  cone  were  inverted,  the  opposite  half  of  the  base 
would  be  shaded,  for  then  the  base  would  be  light,  whereas  it  is 
now  dark.  In  Nos.  7 and  8 the  shade  lines  of  a cylinder  and  a 
circular  hole  are  contrasted. 


In  No.  7 it  is  clear  that  the  light  would  strike  inside  on  the 
further  side  of  the  hole,  commencing  half  way  where  the  45°  lines 


5 6 7 8 


Fig.  23. 

are  tangent.  The  other  half  of  the  inner  surface  would  be  dark, 
hence  the  position  of  the  shade  line.  The  shade  line  then  enables 
us  to  tell  at  a glance  whether  a circle  represents  a hub  or  boss,  or 
depression  or  hole.  Fig.  24  represents  plan,  elevation  and  profile 
view  of  a square  prism.  Here  as  before,  the  view  showing  the 
end  is  the  one  used  to  determine  the  light  and  dark  surfaces,  and 
then  the  shade  lines  put  in  accordingly. 


100 


MECHANICAL  DRAWING. 


19 


In  putting  on  the  shade  lines,  the  extra  width  of  line  is  put 
inside  the  figure,  not  outside.  In  shading  circles,  the  shade  line 

o'  o' 

is  made  of  varying  width,  as  shown  in  the  figures.  The  method 
of  obtaining  this  effect  by  the  compass  is  to  keep  the  same  radius, 
but  to  change  the  center  slightly  in  a direction  parallel  to  the  rays 
of  light,  as  shown  at  A and  B in  No.  2 of  Fig.  24. 

No.  2. 


INTERSECTION  AND  DEVELOPHENT. 

If  one  surface  meets  another  at  some  angle,  an  intersection  is 
produced.  Either  surface  may  be  plane,  or  curved.  If  both  are 
plane,  the  intersection  is  a straight  line  ; if  one  is  curved,  the 
intersection  is  a curve,  except  in  a few  special  cases  ; and  if  both 
are  curved,  the  intersection  is  usually  curved. 

In  the  latter  case,  the  entire  curve  does  not  always  lie  in  the 
same  planes.  If  all  points  of  any  curve  lie  in  the  same  plane,  it 
is  called  a plane  curve.  A plane  intersecting  a curved  surface 
must  always  give  either  a plane  curve  or  a straight  line. 

In  Fig.  25  a square  pyramid  is  cut  by  a plane  A parallel  to  the 
horizontal.  This  plane  cuts  from  the  pyramid  a four-sided  figure, 
the  four  corners  of  which  will  be  the  points  where  A cuts  the  four 
slanting  edges  of  the  solid.  The  plane  intersects  edge  o b at  point  4^ 
in  elevation.  This  point  must  be  found  in  plan  vertically  below  on 


107 


20 


MECHANICAL  DRAWING. 


the  horizontal  projection  of  line  o b , that  is,  at  point  4A  Edge 
o e is  directly  in  front  of  o b,  so  is  shown  in  elevation  as  the  same 
line,  and  plane  A intersects  o e at  point  in  elevation,  found  in 
plan  at  1A  Points  3 and  2 are  obtained  in  the  same  way  The 
intersection  is  shown  in  plan  as  the  square  1 2 3 4,  which  is  also 
its  true  size  as  it  is  parallel  to  the  horizontal  plane.  In  a 

similar  way  the  sections  are  found 
in  Figs.  26  and  27.  It  will  be 
seen  that  in  these  three  cases 
where  the  planes  are  parallel  to 
the  bases,  the  sections  are  of  the 
same  shape  as  the  bases,  and  have 
their  sides  parallel  to  the  edges  of 
the  bases. 

It  is  an  invariable  rule  that 
when  such  a solid  is  cut  by  a plane 
parallel  to  its  base,  the  section  is 
a figure  of  the  same  shape  as  the 
base.  If  then  in  Fig.  28  a right 
cone  is  intersected  by  a plane 
.parallel  to  the  base  the  section 
must  be  a circle,  the  center  of 
which  in  plan  coincides  with  the  apex.  The  radius  must 
equal  o d. 

In  Figs.  29  and  30  the  cutting  plane  is  not  parallel  to  the  base, 
hence  the  intersection  will  not  be  of  the  same  shape  as  the  bas6. 
The  sections  are  found,  however,  in  exactly  the  same  manner  as 
in  the  previous  figures,  by  projecting  the  points  where  the  plane 
intersects  the  edges  in  elevation  on  to  the  other  view  of  the  same 
line. 


INTERSECTION  OF  PLANES  WITH  CONES  OR  CYLINDERS. 

Sections  cut  by  a plane  from  a cone  have  already  been  de- 
fined as  conic  sections.  These  sections  may  be  either  of  the  fol- 
lowing: two  straight  lines,  circle,  ellipse,  parabola,  hyperbola. 

All  except  the  parabola  and  hyperbola  may  also  be  cut  from  a 
cylinder. 

Methods  have  previously  been  given  for  constructing  the 


108 


MECHANICAL  DRAWING. 


21 


22 


MECHANICAL  DRAWING. 


ellipse,  parabola  and  hyperbola  without  projections ; it  will  now 
be  shown  that  they  may  be  obtained  as  actual  intersections. 

In  Fig.  31  the  plane  cuts  the  cone  obliquely.  To  find 
points  on  the  curve  in  plan  take  a series  of  horizontal  planes 


Fig.  3L 


x y z etc.,  between  points  cv  and  dv.  One  of  these  planes,  as  w , 
should  be  taken  through  the  center  of  c d.  The  points  c and  d 
must  be  points  on  the  curve,  since  the  plane  cuts  the  two  contour 
elements  at  these  points.  The  horizontal  projections  of  the  contour 
elements  will  be  found  in  a horizontal  line  passing  through  the  center 
of  the  base ; hence  the  horizontal  projection  of  c and  d will  be 
found  on  this  center  line,  and  will  be  the  extreme  ends  of  the 
curve.  Contour  elements  are  those  forming  the  outline. 


110 


MECHANICAL  DRAWING. 


23 


The  plane  x cuts  the  surface  of  the  cone  in  a circle,  as  it  is 
parallel  to  the  base,  and  the  diameter  of  the  circle  is  the  distance 
between  the  points  where  x crosses  the  two  contour  elements. 
This  circle,  lettered  x on  the  plan,  has  its  center  at  the  horizontal 
projection  of  the  apex.  The  circle  x and  the  curve  cut  by  the  plane 
are  both  on  the  surface  of  the  cone,  and  their  vertical  projec- 
tions intersect  at  the  point  2.  Also  the  circle  x and  the  curve 
must  cross  twice,  once  on  the  front  of  the  cone  and  once  on  the 
back.  Point  2 then  represents  two  points  which  are  shown  in 
plan  directly  beneath  on  the  circle  x,  and  are  points  on  the  re- 
quired intersection.  Planes  y and  z,  and  as  many  more  as  may 
be  necessary  to  determine  the  curve  accurately,  are  used  in  the 
same  way.  The  curve  found  is  an  ellipse.  The  student  will 
readily  see  that  the  true  size  of  this  ellipse  is  not  shown  in  the 
plan,  for  the  plane  containing  the  curve  is  not  parallel  to  the 
horizontal. 

In  order  to  find  the  actual  size  of  the  ellipse,  it  is  necessary 
to  place  its  plane  in  a position  parallel  either  to  the  vertical  or  to 
the  horizontal.  The  actual  length  of  the  long  diameter  of  the 
ellipse  must  be  shown  in  elevation,  dv,  because  the  line  is 
parallel  to  the  vertical  plane.  The  plane  of  the  ellipse  then  may 
be  revolved  about  cv  dv  as  an  axis  until  it  becomes  parallel  to  V, 
when  its  true  size  will  be  shown.  For  the  sake  of  clearness  of 
construction,  c*>  c?u  is  imagined  moved  over  to  the  position  c'  d\ 
parallel  to  cv  d*.  The  lines  1 — 1,  2 — 2,  8 — 8 on  the  plan  show  the 
true  width  of  the  ellipse,  as  these  lines  are  parallel  to  H,  but  are 
projected  closer  together  than  their  actual  distances.  In  elevation 
these  lines  are  shown  as  the  points  1,  2,  3,  at  their  true  distance 
apart.  Hence  if  the  ellipse  is  revolved  around  its  axis  c*>  the 
distances  1 — 1,  2 — 2,  3 — 3 will  appear  perpendicular  to  cv  dv,  and 
the  true  size  of  the  figure  be  shown.  This  construction  is  made  on 
the  left,  where  1' — 1',  2r — 2' and  3' — 3'  are  equal  in  length  to  1 — 1, 
2 — 2,  3 — 3 on  the  plan. 

In  Fig.  32  a plane  cuts  a cylinder  obliquely.  This  is  a 
simpler  case,  as  the  horizontal  projection  of  the  curve  coincides 
with  the  base  of  the  cylinder.  To  obtain  the  true  size  of  the 
section,  which  is  an  ellipse,  any  number  of  points  are  assumed  on 
the  plan  and  projected  up  on  the  cutting  plane,  at  1,  2,  3,  etc. 


Ill 


24 


MECHANICAL  DRAWING. 


The  lines  drawn  through  these  points  perpendicular  to  1 7 are 
made  equal  in  length  to  the  corresponding  distances  2f — 2',  8' — 3' 
etc.,  on  the  plan,  because  2' — 2'  is  the  true  width  of  curve  at  2. 

If  a cone  is  intersected  by  a plane  which  is  parallel  to  only 

one  of  the  elements,  as  in 
Fig.  33,  the  resulting  curve 
is  the  parabola,  the  construc- 
tion of  which  is  exactly  simi- 
lar to  that  for  the  ellipse  as 
given  in  Fig.  31.  If  the 
intersecting  plane  is  parallel 
to  more  than  one  element,  or 
is  parallel  to  the  axis  of  the 
cone,  a hyperbola  is  produced. 

In  Fig.  34,  the  vertical 
plane  A is  parallel  to  the  axis 
of  the  cone.  In  this  instance 
the  curve  when  found  will 
appear  in  its  true  size,  as 
plane  A is  parallel  to  the 
vertical.  Observe  that  the 
highest  point  of  the  curve  is 
found  by  drawing  the  circle 
X on  the  plan  tangent  to  the 
given  plane.  One  of  the 
points  where  this  circle  crosses 
the  diameter  is  projected  up 
to  the  contour  element  of  the 
cone,  and  the  horizontal  plane  X drawn.  Intermediate  planes 
Y,  Z,  etc.,  are  chosen,  and  corresponding  circles  drawn  in  plan. 
The  points  where  these  -circles  are  crossed  by  the  plane  A are 
points  on  the  curve,  and  these  points  are  projected  up  to  the 
elevation  on  the  planes  Y,  Z,  etc. 

DEVELOPHENTS. 

The  development  of  a surface  is  the  true  size  and  shape  ot 
the  surface  extended  or  spread  out  on  a plane.  If  the  surface  to 
be  developed  is  of  such  a character  that  it  may  be  flattened  out 


Fig.  32. 


112 


MECHANICAL  DRAWING. 


25 


without  tearing  or  folding,  we  obtain  an  exact  development,  as  in 
case  of  a cone  or  cylinder,  prism  or  pyramid.  If  this  cannot  be 
done,  as  with  the  sphere,  the  development  is  only  approximate. 

In  Older  to  find  the  development  of  the  rectangular  prism  in 
Fig  35,  the  back  face,  1 2 7 6,  is  supposed  to  be  placed  in  contact 


Fig.  33. 


with  some  plane,  then  the  prism  turned  on  the  edge  2 7 until  the 
side  23  8 7 is  in  contact  with  the  same  plane,  then  this  continued 
until  all  four  faces  have  been  placed  on  the  same  plane.  The 
rectangles  1 4 3 2 and  6 7 8 5 are  for  the  top  and  bottom  respec- 
tively. The  development  then  is  the  exact  size  and  shape  of  a 
covering  for  the  prism.  If  a rectangular  hole  is  cut  through  the 
prism,  the  openings  in  the  front  and  back  faces  will  be  shown  in 
the  development  in  the  centers  of  the  two  broad  faces. 

The  development  of  a right  prism,  then,  consists  of  as  many 


113 


26 


MECHANICAL  DRAWING. 


rectangles  joined  together  as  the  prism  has  sides,  these  rectangles 
being  the  exact  size  of  the  faces  of  the  prism,  and  in  addition  two 
polygons  the  exact  size  of  the  bases.  It  will  be  found  helpful  in 
developing  a solid  to  number  or  letter  all  of  the  corners  on  the 

projections,  then 
designate  each  face 
when  developed  in 
the  same  way  as  in 
the  figure. 

If  a cone  be 
placed  on  its  side  on 
a plane  surface,  one 
element  will  rest  on 
the  surface.  If  now 
the  cone  be  rolled  on 
the  plane,  the  vertex 
remaining  stationary, 
until  the  same  ele- 
ment is  in  contact 
again,  the  space  rolled 
over  will  represent 
the  development  of 
the  convex  surface 
of  the  cone.  A,  Fig. 
86,  is  a cone  cut  by  a 
plane  parallel  to  the 
base.  In  B,  let  the 
vertex  of  the  cone  be 
cone  coincide  with  Y A I. 
The  length  of  this  element  is  taken  from  the  elevation  A,  of 
either  contour  element.  All  of  the  elements  of  the  cone  are  of 
the  same  length,  so  when  the  cone  is  rolled  each  point  of  the  base 
as  it  touches  the  plane  will  be  at  the  same  distance  from  the 
vertex.  From  this  it  follows  that  the  development  of  the  base 
will  be  the  arc  of  a circle  of  radius  equal  to  the  length  of  an 
element.  To  find  the  length  of  this  arc  which  is  equal  to  the 
distance  around  the  base,  divide  the  plan  of  the  circumference 
of  the  base  into  any  number  of  equal  parts,  as  twelve,  then 


114 


MECHANICAL  DRAWING. 


'M 


with  the  length  of  one  of  these  parts  as  radius,  lay  off  twelve 
spaces,  1 ....13,  join  1 and  13  with  Y,  and  the  sector  is  the  development 
of  the  cone  from  vertex  to  base.  To  represent  on  the  development 


8 6 


Fig.  35. 


the  circle  cut  by  the  section  plane,  take  as  radius  the  length  of 
the  element  from  the  vertex  to  D,  and  with  Y as  center  describe 


an  arc.  The  development  of  the  frustum  of  the  cone  will  be  the 
portion  of  the  circular  ring.  This  of  course  does  not  include  the 


115 


28 


MECHANICAL  DRAWING. 


development  of  the  bases,  which  would  he  simply  two  circles  the 
same  sizes  as  shown  in  plan. 

A and  B,  Fig.  87,  represent  the  plan  and  elevation  of  a 
regular  triangular  pyramid  and  its  development.  If  face  C is 
placed  on  the  plane  its  true  size  will  be  shown  at  C in  the  devel- 
opment. The  true  length  of  the  base  of  triangle  C is  shown:  in 
the  plan.  The  slanting  edges,  however,  not  being  parallel  to  the 
vertical,  are  not  shown  in  elevation  in  their  true  length.  It  be- 
comes necessary  then,  to  find  the  true  length  of  one  of  these  edges 
as  shown  in  Fig.  6,  after  which  the  triangle  may  be  drawn  in  its 
full  size  at  C in  the  development.  As  the  pyramid  is  regular, 
three  equal  triangles  as  shown  developed  at  C,  D and  E,  together 
with  the  base  F,  constitute  the  development. 

If  a right  circular  cylinder  is  to  be  developed,  or  rolled  upon 
a plane,  the  elements,  being  parallel,  will  appear  as  parallel  lines, 


and  the  base,  being  perpendicular  to  the  elements,  will  develop  as 
a straight  line  perpendicular  to  the  elements.  The  width  of  the 
development  will  be  the  distance  around  the  cylinder,  or  the  cir- 
cumference of  the  base.  The  base  of  the  cylinder  in  Fig.  88,  is 
divided  into  twelve  equal  parts,  12  8,  etc.  Commencing  at  point 
1 on  the  development  these  twelve  equal  spaces  are  laid  along 
the  straight  line,  giving  the  development  of  the  base  of  the  cylin- 
der, and  the  total  width.  To  find  the  development  of  the  curve 
cut  by  the  oblique  plane,  draw  in  elevation  the  elements  corre- 
sponding to  the  various  divisions  of  the  base,  and  note  the  points 


116 


MECHANICAL  DRAWING. 


29 


where  they  intersect  the  oblique  plane.  As  we  roll  the  cylinder 
beginning  at  point  1,  the  successive  elements  1,  12,  11,  etc.,  will 
appear  at  equal  distances  apart,  and  equal  in  length  to  the  lengths 
of  the  same  elements  in  elevation.  Thus  point  number  10  on  the 
development  of  the  curve  is  found  by  projecting  horizontally  across 
from  10  in  elevation.  It  will  be  seen  that  the  curve  is  symmetri- 
cal, the  half  on  the  left  of  7 being*  similar  to  that  on  the  right. 

7 O O 

The  development  of  any  curve  whatever  on  the  surface  of  the 
cylinder  may  be  found  in  the  same  manner. 

The  principle  of  cylinder  development  is  used  in  laying  out 
elbow  joints,  pipe  ends  cut  off  obliquely,  etc.  In  Fig.  39  is  shown 
plan  and  elevation  of  a three-piece  elbow  and  collar,  and  develop- 


ments of  the  four  pieces.  In  order  to  construct  the  various  parts 
making  up  the  joint,  it  is  necessary  to  know  what  shape  and  size 
must  be  marked  out  on  the  flat  sheet  metal  so  that  when  cut  out 
and  rolled  up  the  three  pieces  will  form  cylinders  with  the  ends 
fitting  together  as  required.  Knowing  the  kind  of  elbow  desired, 
we  first  draw  the  plan  and  elevation,  and  from  these  make  the 
developments.  Let  the  lengths  of  the  three  pieces  A,  B and  C 
be  the  same  on  the  upper  outside  contour  of  the  elbow,  the  piece 
B at  an  angle  of  45°;  the  joint  between  A and  B bisects  the 
angle  between  the  two  lengths,  and  in.  the  same  way  the  joint 
between  B and  C.  The  lengths  A and  C will  then  be  the  same, 


117 


30 


MECHANICAL  DRAWING. 


and  one  pattern  will  answer  for  both.  The  development  of  A 
is  made  exactly  as  just  explained  for  Fig.  38,  and  this  is  also  the 
development  of  C. 

It  should  be  borne  in  mind  that  in  developing  a cylinder  we 
must  always  have  a base  at  right  angles  to  the  elements,  and  if 
the  cylinder  as  given  does  not  have  such  a base,  it  becomes  neces- 
sary to  cut  the  cylinder  by  a plane  perpendicular  to  the  elements, 
and  use  the  intersection  as  a base.  This  point  must  be  clearly 
understood  in  order  to  proceed  intelligently.  A section  at  right 
angles  to  the  elements  is  the  only  section  which  will  unroll  in  a 


straight  line,  and  is  therefore  the  section  from  which  we  must 
work  in  developing  other  sections.  As  B has  neither  end  at  right 
angles  to  its  length,  the  plane  X is  drawn  at  the  middle  and  per* 
pendicular  to  the  length.  B is  the  same  diameter  pipe  as  C and 
A,  so  the  section  cut  by  X will  be  a circle  of  the  same  diameter 
as  the  base  of  A,  and  its  development  is  shown  at  X. 

From  the  points  where  the  elements  drawn  on  the  elevation 
of  A meet  the  joint  between  A and  B,  elements  are  drawn  on  B, 


118 


MECHANICAL  DRAWING. 


0 t 

01 


which  are  equally  spaced  around  B the  same  as  on  A.  The  spaces 
then  laid  off  along  X are  the  same  as  given  on  the  plan  of  A. 
Commencing  with  the  left-hand  element  in  B,  the  length  of  the 
upper  element  between  X and  the  top  corner  of  the  elbow  is  laid 
off  above  X,  giving  the  first  point  in  the  development  of  the  end 
of  B fitting  with  C.  The  lengths  of  the  other  elements  in  the 
elevation  of  B are  measured  in  the  same  way  and  laid  off  from  X. 
The  development  of  the 
other  end  of  the  piece 
B is  laid  off  below  X, 
using  the  same  distances, 
since  X is  half  way  be- 
tween the  ends.  The 
development  of  the 
collar  is  simply  the  de_ 
velopment  of  the  frus- 
tum of  a cone,  which  has 
already  been  explained, 

Fig.  86.  The  joint  be- 
tween B and  C is  shown 
in  plan  as  an  ellipse,  the 
construction  of  which 
the  student  should  be 
able  to  understand  from 
a study  of  the  figure. 

The  intersection  of 
a rectangular  prism  and 
pyramid  is  shown  in  Fig.  40.  The  base  b c d e of  the  pyramid  is 
shown  dotted  in  plan,  as  it  is  hidden  by  the  prism.  All  four  edges 
of  the  pyramid  pass  through  the  top  of  the  prism,  1,  2,  3,  4.  As 
the  top  of  the  prism  is  a horizontal  plane,  the  edges  of  the  pyramid 
are  showm  passing  through  the  top  in  elevation  at  xv  g*>  kv  iv.  These 
four  points  might  be  projected  to  the  plan  on  the  four  edges  of  the 
pyramid;  but  it  is  unnecessary  to  project  more  than  one,  since  the 
general  principle  applies  here  that  if  a cone,  pyramid,  prism  or 
cylinder  be  cut  by  a plane  parallel  to  the  base,  the  section  is  a 
figure  parallel  and  similar  to  the  base.  The  one  point  xv  is  there- 
fore projected  down  to  a b in  plan,  giving  xh,  and  with  this  as 


av 


119 


32 


MECHANICAL  DRAWING. 


one  corner,  the  square  xh  gh  i h kli  is  drawn,  its  sides  parallel  to  the 
edges  of  the  base.  This  square  is  the  intersection  of  the  pyramid 
with  the  top  of  the  prism. 

The  intersection  of  the  pyramid  with  the  bottom  of  the  prism 
is  found  in  like  manner,  by  taking  the  point  where  one  edge  of 
the  pyramid  as  a b passes  through  the  bottom  of  the  prism  shown 
in  elevation  as  point  m»,  projecting  down  to  mh  on  ah  bh,  and 
drawing  the  square  mh  nJl  oh  ph  parallel  to  the  base  of  the  pyramid. 
These  two  squares  constitute  the  entire  intersection  of  the  two 
solids,  the  pyramid  going  through  the  bottom  and  coming  out  at 
the  top  of  the  prism.  As  much  of  the  slanting  edges  of  the 


pyramid  as  are  above  the  prism  will  be  seen  in  plan,  appearing  as 
the  diagonals  of  the  small  square,  and  the  rest  of  the  pyramid, 
being  below  the  top  surface  of  the  prism,  will  be  dotted  in  plan. 

Fig.  41  is  the  development  of  the  rectangular  prism,  show- 
ing the  openings  in  the  top  and  bottom  surfaces  through  which 
the  pyramid  passed.  The  development  of  the  top  and  bottom, 
back  and  front  faces  will  be  four  rectangles  joined  together,  the 
same  sizes  as  the  respective  faces.  Commencing  with  the  bottom 
face  5 6 7 8,  next  would  come  the  back  face  6127,  then  the  top, 
etc.  The  rectangles  at  the  ends  of  the  top  face  1 2 3 4 are  the 
ends  of  the  prism.  These  might  have  been  joined  on  any  other 


120 


MECHANICAL  DRAWING 


33 


face  as  well.  Now  find  the  development  of  the  square  in  the  bottom 
5 6 7 8.  As  the  size  will  be  the  same  as  in  projection,  it  only  re- 
mains to  determine  its  position.  This  position,  however,  will 
have  the  same  relation  to  the  sides  of  the  rectangle  as  in  the  plan. 
The  center  of  the  square  in  this  case  is  in  the  center  of  the  face. 
To  transfer  the  diagonals  of  the  square  to  the  development,  extend 
them  in  plan  to  intersect  the  edges  of  the  prism  in  points  9,  10, 
11  and  12.  Take  the  distance  from  5 to  9 along  the  edge  5 6, 
and  lay  it  on  the  development  from  5 along  5 6,  giving  point  9. 
Point  10  located  in  the  same  way  and  connected  with  9,  gives  the 
position  of  one  diagonal.  The  other  diagonal  is  obtained  in  a 
similar  way,  then  the  square  constructed  on  these  diagonals.  The 
same  method  is  used  for  locating  the  small  square  on  the  top  face. 

If  the  intersection  of  a cylinder  and  prism  is  to  be  found,  we 
may  either  obtain  the  points  where  elements  of  the  cylinder  pierce 
the  prism,  or  where  edges  and  lines  parallel  to  edges  on  the  sur* 
face  of  the  prism  cut  the  cylinder. 

A series  of  parallel  planes  may  also  be  taken  cutting  curves 
from  the  cylinder  and  straight  lines  from  the  prism ; the  intersec- 
tions give  points  on  the  intersection  of  the  two  solids. 

Fig.  42  represents  a triangular  prism  intersecting  a cylinder. 
The  axis  of  the  prism  is  parallel  to  V and  inclined  to  H.  Starting 
with  the  size  and  shape  of  the  base,  this  is  laid  off  at  a{  bh  ch , and 
the  altitude  of  the  triangle  taken  and  laid  off  at  av  cv  in  elevation, 
making  right  angles  with  the  inclination  of  the  axis  to  H.  The 
plan  of  the  prism  is  then  constructed.  To  find  the  intersection  of 
the  two  solids,  lines  are  drawn  on  the  surface  of  the  prism  parallel 
to  the  length  and  the  points  where  these  lines  and  the  edges 
pierce  the  cylinder  are  obtained  and  joined,  giving  the  curve. 

The  top  edge  of  the  prism  goes  into  the  top  of  the  cylinder. 
This  point  will  be  shown  in  elevation,  since  the  top  of  the  cylinder 
is  a plane  parallel  to  H and  perpendicular  to  V,  and  therefore 
projected  on  V as  a straight  line.  The  upper  edge,  then,  is  found 
to  pass  into  the  top  of  the  cylinder  at  point  o,  ov  and  oh.  The 
intersection  of  the  two  upper  faces  of  the  prism  with  the  top  of 
the  cylinder  will  be  straight  lines  drawn  from  point  o and  will  be 
shown  in  plan.  If  we  can  find  where  another  line  of  the  surface 
o a h 14  pierces  the  upper  base  of  the  cylinder,  this  point  joined 


121 


Fig.  43. 


34 


MECHANICAL  DRAWING. 


with  o will  determine  the  intersection  of  this  face  with  the  top  of 
the  cylinder.  A surface  may  always  be  produced,  if  necessary, 
to  find  an  intersection. 


Edge  a b pierces  the  plane  of  the  top  of  the  cylinder  at  point 


d , seen  in  elevation  ; therefore  the  line  joining  this  point  with  o is 
the  intersection  of  one  upper  face  of  the  prism  with  the  upper 


122 


MECHANICAL  DRAWING. 


35 


base  of  the  cylinder.  The  only  part  of  this  line  needed,  of  course, 
is  within  the  actual  limits  of  the  base,  that  is  o 9.  The  intersec- 
tion o 8 of  the  other  top  face  is  found  by  the  same  method.  On 
the  convex  surface  of  the  cylinder  there  will  be  three  curves,  one 
for  each  face  of  the  prism.  Points  b and  9 on  the  upper  base  of 
the  cylinder,  will  be  where  the  curves  for  the  two  upper  faces  will 
begin.  The  point  d is  found  on  the  revolved  position  of  the  base 
at  t?,,  and  d{  b is  divided  into  the  equal  parts  d{  — ep  ex  — /j,  etc., 
which  revolve  back  to  d\  eh,fh  and  gh.  The  divisions  are  made 
equal  merely  for  convenience  in  developing.  The  vertical  pro- 
jections of  d,  e , etc.,  are  found  on  the  vertical  projection  of  a b, 
directly  above  dh , e\  etc.,  or  may  be  found  by  taking  from  the 
revolved  position  of  the  base,  the  perpendiculars  from  dx  e , etc.,  to 
ch  bh  and  laying  them  off  in  elevation  from  bv  along  bv  av.  Lines 
such  as  f 12,  m 5,  etc.,  parallel  to  a o are  drawn  in  plan  and  eleva- 
tion. Points  ih  kh  mh  nh  are  taken  directly  behind  dh  eh  fh  gh 
hence  their  vertical  projections  coincide.  Points  nx  m,  /q  and  z,  are 
formed  by  projecting  across  from  nh  mh  Jch  and  ih. 

The  convex  surface  of  the  cylinder  is  perpendicular  to  H,  so 
the  points  where  the  lines  on  the  prism  pierce  it  will  be  projected 
on  plan  as  the  points  Avhere  these  lines  cross  the  circle,  14,  13, 12, 

11 .3.  The  vertical  projections  of  these  points  are  found  on 

the  corresponding  lines  in  elevation,  and  the  curves  drawn  through. 
The  curve  3,  4.. ..8  must  be  dotted,  as  it  is  on  the  back  of  the 
cylinder.  The  under  face  of  the  prism,  which  ends  with  the  line 
b c,  is  perpendicular  to  the  vertical  plane,  so  the  curve  of  intersec 
tion  will  be  projected  on  V as  a straight  line.  Point  14  is  one 
end  of  this  curve.  3 the  other  end,  and  the  curve  is  projected  in 
elevation  as  the  straight  line  from  14  to  the  point  where  the  lower 
edge  of  the  prism  crosses  the  contour  element  of  the  cylinder. 

Fig.  43  gives  the  development  of  the  right-hand  half  of  the 
cylinder,  beginning  with  number  1 . As  previously  explained,  the 
distance  betAveen  the  elements  is  shown  in  the  plan,  as  1 — 2,  2 — 3, 
3 — 4 and  so  on.  These  spaces  are  laid  off  in  the  development 
along  a straight  line  representing  the  deA^elopment  of  the  base, 
and  from  these  points  the  elements  are  drawn  perpendicularly. 

The  lengths  of  the  elements  in  the  development  from  the  base 
to  the  curve  are  exactly  the  same  as  on  the  elevation,  as  the 


183 


36 


MECHANICAL  DRAWING. 


elevation  gives  the  true  lengths.  If  then  the  development  of  the 
base  is  laid  off  along  the  same  straight  line  as  the  vertical  projec- 
tion of  the  base,  the  points  in  elevation  maj^  be  projected  across 
with  the  T-square  to  the  corresponding  elements  in  the  develop- 
ment. The  points  on  the  curve  cut  by  the  under  face  of  the 
prism  are  ou  the  same  elements  as  the  other  curves,  and  their 
vertical  projections  are  on  the  under  edge  of  the  prism,  hence 
these  points  are  projected  across  for  the  development  of  the  lower 
curve. 

In  Fig.  44  is  given  the  development  of  the  prism  from  the 
right-hand  end  as  far  as  the  intersection  with  the  cylinder,  begin- 


14 


ning  at  the  left  with  the  top  edge  a o,  the  straight  line  a b c a 
being  the  development  of  the  base.  As  this  must  be  the  actual 
distance  around  the  base,  the  length  is  taken  from  the  true  size 
of  the  base,  a,  bh  ch.  The  parallel  lines  drawn  on  the  surfaces  of 
the  prism  must  appear  on  the  development  their  true  distances 
apart,  hence  the  distances  ax  dr  d l e,,  etc.,  are  made  equal  to 
a d,  de,  etc.  on  the  development.  The  actual  distances  between  the 
parallel  lines  on  the  bottom  face  of  the  prism  are  shown  along 
the  edge  of  the  base,  bh  ch.  Perpendicular  lines  are  drawn  from 
the  points  of  division  on  the  development. 

The  position  of  the  developed  curve  is  found  by  laying  off 
the  true  lengths  on  the  perpendiculars.  These  true  lengths  (of 
the  parallel  lines)  are  not  shown  in  plan,  as  the  lines  are  not 
parallel  to  the  horizontal  plane,  but  are  found  in  elevation.  The 
length  oa  on  the  development  is  equal  to  av  d 10  to  dv  1 0,  and 


124 


MECHANICAL  DRAWING 


37 


so  on  for  all  the  rest.  Point  9ys  found  as  follows:  on  the  projec- 
tions, the  straight  line  from  o to  d passes  through  point  9,  and  the 
true  distance  from  o to  9 is  shown  in  plan.  All  that  is  necessary, 
then,  is  to  connect  o and  d on  the  development,  and  lay  off  from  o 
the  distance  0h9.  Number  8 is  found  in  the  same  way. 

ISOMETRIC  PROJECTION. 

Heretofore  an  object  has  been  represented  by  two  or  more 
projections.  Another  system,  called  isometrical  drawing,  is  used 
to  show  in  one  view  the  three  dimensions  of  an  object,  length  (or 
height),  breadth,  and  thickness.  An  isometrical  drawing  of  an 
object,  as  a cube,  is  called  for  brevity  the  “ isometric  ” of  the  cube. 


Fig.  45. 


To  obtain  a view  which  shows  the  three  dimensions  in  such  a 
way  that  measurements  can  be  taken  from  them,  draw  the  cube  in 
the  simple  position  shown  at  the  left  of  Fig.  45,  in  which 
it  rests  on  H with  two  faces  parallel  to  V ; the  diagonal  from  the 
front  upper  right-hand  corner  to  the  back  lower  left-hand  corner  is 
indicated  by  the  dotted  line.  Swing  the  cube  around  until  the 
diagonal  is  parallel  with  V as  shown  in  the  second  position.  Here 
the  front  face  is  at  the  right.  In  the  third  position  the  lower  end 
of  the  diagonal  has  been  raised  so  that  it  is  parallel  to  H,  becoming 
thus  parallel  to  both  planes.  The  plan  is  found  by  the  principles 
of  projection,  from  the  elevation  and  the  preceding  plan.  The  front 
face  is  now  the  lower  of  the  two  faces  shown  in  the  elevation. 
From  this  position  the  cube  is  swung  around,  using  the  corner 


125 


38 


MECHANICAL  DRAWING 


resting  on  the  H as  a pivot,  until  the  diagonal  is  perpendiculai 
to  V but  still  parallel  to  H.  The  plan  remains  the  same,  except  as 
regards  position;  while  the  elevation,  obtained  by  projecting  across 
from  the  previous  elevation,  gives  the  isometrical  projection  of  the 
cube.  The  front  face  is  now  at  the  left. 

In  the  last  position,  as  one  diagonal  is  perpendicular  to  V,  it 
follows  that  all  the  faces  of  the  cube  make  equal  angles  with  V, 
hence  are  projected  on  that  plane  as  equal  parallelograms.  For  the 
same  reason  all  the  edges  of  the  cube  are  projected  in  elevation  in 
equal  lengths,  but,  being  inclined  to  V,  appear  shorter  than  they 
actually  are  on  the  object.  Since  they  are  all  equally  foreshortened 
and  since  a drawing  may  be  made  at  any  scale,  it  is  customary  to 

make  all  the  isometrical  lines  of  a 
drawing  full  length.  This  will  give 
the  same  proportions,  and  is  much 
the  simplest  method.  Herein  lies 
the  distinction  between  an  isomet- 
rical projection  and  an  isometric- 
drawing. 

It  will  be  noticed  that  the 
figure  can  be  inscribed  in  a circle, 
and  that  the  outline  is  a perfect 
hexagon.  Hence  the  lines  showing 
breadth  and  length  are  30°  lines, 
while  those  showing  height  are 
vertical. 

Fig.  46  shows  the  isometric  of  a cube,  1 inch  square.  All  of 
the  edges  are  shown  in  their  true  length,  hence  all  the  surfaces 
appear  of  the  same  size.  In  the  figure  the  edges  of  the  base  are 
inclined  at  30°  with  a T-square  line,  but  this  is  not  always  the  case. 
For  rectangular  objects,  such  as  prisms,  cubes,  etc.,  the  base 
edges  are  at  30°  only  when  the  prism  or  cube  is  supposed  to  be  in 
the  simplest  possible  position.  The  cube  in  Fig.  46  is  supposed  to 
be  in  the  position  indicated  by  plan  and  elevation  in  Fig.  47,  that 
is,  standing  on  its  base,  with  two  faces  parallel  to  the  vertical 
plane. 

If  the  isometric  of  the  cube  in  the  position  of  Fig.  48  were 
required,  it  could  not  be  drawn  with  the  base  edges  at  30° ; neither 


126 


MECHANICAL  DRAWING 


39 


would  these  edges  appear  in  their  true  lengths.  It  follows,  then, 
that  in  isometrical  drawing,  true  lengths  appear  only  as  30°  lines 
or  as  vertical  lines.  Edges  or  lines  that  in  actual  projection  are 
either  parallel  to  the  ground  line  or  perpendicular  to  V,  are  drawn 
in  isometric  as  30°  lines,  full  length;  and  those  that  are  actually 
vertical  are  made  vertical  in  isometric,  also  full  length. 

In  Fig.  45,  lines  such  as  the  front  vertical  edges  of  the  cube 
and  the  two  base  edges  are  called  the  three  isometric  axes.  The 
isometric  of  objects  in  oblique  positions,  as  in  Fig.  48,  can  be  con- 


Fig.  47.  Fig.  48. 

strutted  only  by  reference  to  their  projections,  by  methods  which 
will  be  explained  later. 

In  isometric  drawing  small  rectangular  objects  are  more  satis- 
factorily represented  than  large  curved  ones.  In  woodwork,  mor- 
tises and  joints  and  various  parts  of  framing  are  well  shown  in 
isometric.  This  system  is  used  also  to  give  a kind  of  bird's-eye 
view  of  the  mills  or  factories.  It  is  also  used  in  making  sketches 
of  small  rectangular  pieces  of  machinery,  where  it  is  desirable  to 
give  shape  and  dimensions  in  one  view. 

In  isometric  drawing  the  direction  of  the  ray  of  light  is 
parallel  to  that  diagonal  of  a cube  which  runs  from  the  upper  left 
corner  to  the  lower  right  corner,  as  4V-7V  in  the  last  elevation  of 
Fig.  45.  This  diagonal  is  at  30° ; hence  in  isometrical  drawing 
the  direction  of  the  light  is  at  30°  downward  to  the  right.  From 


127 


40 


MECHANICAL  DRAWING 


this  it  follows  that  the  top  and  two  left-hand  faces  of  the  cube  are 
light,  the  others  dark.  This  explains  the  shade  lines  in  Fig.  45. 

In  Fig.  45,  the  top  end  of  the  diagonal  which  is  parallel  to  the 
ray  of  light  in  the  first  position  is  marked  4,  and  traced  through 
to  the  last  or  isometrical  projection,  4V.  It  will  be  seen  that  face 
3V  4V  5V  8V  of  the  isometric  projection  is  the  front  face  of  the  cube 
in  the  first  view;  hence  we  may  consider  the  left  front  face  of  the 
isometric  cube  as  the  front.  This  is  not  absolutely  necessary, 
but  by  so  doing  the  isometric  shade  edges  are  exactly  the  same 
as  on  the  original  projection. 


f 


Fig.  49  shows  a cube  with  circles  inscribed  in  the  top  and 
two  side  faces.  The  isometric  of  a circle  is  an  ellipse,  the  exact 
construction  of  which  would  necessitate  finding  a number  of  points; 
for  this  reason  an  approximate  construction  by  arcs  of  circles  is 
often  made.  In  the  method  of  Fig.  49,  four  centers  are  used. 
Considering  the  upper  face  of  the  cube,  lines  are  drawn  from  the 
obtuse  angles  f and  e,  to  the  centers  of  the  opposite  sides. 

The  intersections  of  these  lines  give  points  g and  A,  which 
serve  as  centers  for  the  ends  of  the  ellipse.  With  center  g and 
radius  g a , the  arc  a d is  drawn;  and  with/*  as  center  and  radius 
f d , the  arc  d c is  described,  and  the  ellipse  finished  by  using 
centers  h and  e.  This  construction  is  applied  to  all  three  faces. 

Fig.  50  is  the  isometric  of  a cylinder  standing  on  its  base. 


128 


MECHANICAL  DRAWING 


41 


Notice  that  the  shade  line  on  the  top  begins  and  ends  where 
T-square  lines  would  be  tangent  to  the  curve,  and  similarly  in  the 
case  of  the  part  shown  on  the  base.  The  explanation  of  the  shade 
is  very  similar  to  that  in  pro- 
jections. Given  in  projections 
a cylinder  standing  on  its 
base,  the  plan  is  a circle,  and 
the  shade  line  is  determined 
by  applying  the  45°  triangle 
tangent  to  the  circle.  This  is 
done  because  the  45°  line  is 
the  projection  of  the  ray  of 
light  on  the  plane  of  the 
base. 

In  Fig.  49,  the  diagonal  m l may  represent  the  ray  of  light 
and  its  projection  on  the  base  is  seen  to  be  k l , the  diagonal  of  the 
base,  a T-square  line.  Hence,  for  the  cylinder  of  Fig.  50,  apply 
tangent  to  the  base  and  also  to  the  top  a line  parallel  to  the 
projection  of  the  ray  of  light  on  these  planes,  that  is,  a T-square 
line,  and  this  will  mark  the  beginning  and  ending  of  the  shade  line. 

In  Fig.  49  the  projection  of  the  ray  of  light  diagonal  m l on 

the  right-hand  face  is  e Z,  a 30° 
line;  hence,  in  Fig.  51,  where  the 
base  is  similarly  placed,  apply 
the  30°  triangle  tangent  as  indi- 
cated, determining  the  shade  line 
of  the  base.  If  the  ellipse  on 
the  left-hand  face  of  the  cube  were 
the  base  of  a cone  or  cylinder 
extending  backward  to  the  right, 
the  same  principle  would  be  used. 

The  projection  of  the  cube  diagonal  m l on  that  face  is  m n,  a 
60°  line;  hence  the  60°  triangle  would  be  used  tangent  to  the  base 
in  this  last  supposed  case,  giving  the  ends  of  the  shade  line  at 
points  o and  r.  Figs.  52,  53  and  54  illustrate  the  same  idea  with 
respect  to  prisms,  the  direction  of  the  projection  of  the  ray  of  light 
on  the  plane  of  the  base  being  used  in  each  case  to  determine  the 
light  and  dark  faces  and  hence  the  shade  lines. 


120 


42 


MECHANICAL  DRAWING 


In  Fig.  52  a prism  is  represented  standing  on  its  base,  so  that 
the  projection  of  the  cube  diagonal  on  the  base  (that  is,  a T-square 
line)  is  used  to  determine  the  light  and  dark  faces  as  shown. 

The  prism  in  Fig.  53  has  for 
its  base  a trapezium.  The 
projection  of  the  ray  of  light 
on  this  end  is  parallel  to  the 
diagonal  of  the  face;  hence 
the  60°  triangle  applied  par- 
allel to  this  diagonal  shows 
that  faces  a c db  and  a g hb 
are  light,  while  c e f cl  and 
g e f h are  dark,  hence  the 
shade  lines  as  shown. 

The  application  in  Fig. 
54  is  the  same,  the  only 
difference  being  in  the  position  of  the  prism,  and  the  consequent 
difference  in  the  direction  of  the  diagonal. 

Fig.  55  represents  a block  with  smaller  blocks  projecting  from 
three  faces. 

Fig.  56  shows  a framework  of  three  pieces,  two  at  right  angles 
and  a slanting  brace.  The  horizontal  piece  is  mortised  into  the 
upright,  as  indicated  by  the 
dotted  lines.  In  Fig.  57 
the  isometric  outline  of  a 
house  is  represented,  show- 
ing a dormer  window  and 
a partial  hip  roof;  a b is  a 
hip  rafter,  c d a valley.  Let 
the  pitch  of  the  main  roof 
be  shown  at  B,  and  let  m be 
the  middle  point  of  the  top 
of  the  end  wall  of  the 
house.  Then,  by  measuring 
vertically  up  a distance  m l 
equal  to  the  vertical  height 
a n shown  at  B,  a point  on  the  line  of  the  ridge  will  be  found  at  l. 
Line  l i is  equal  to  b h,  and  i h is  then  drawn.  Let  the  pitch  of 


130 


MECHANICAL  DRAWING 


43 


the  end  roof  be  given  at  A.  This  shows  that  the  peak  of  the  roof, 
or  the  end  a of  the  ridge,  will  be  back  from  the  end  wall  a distance 
equal  to  the  base  of  the  triangle  at  A.  Hence  lay  off  from  l this 
distance,  giving  point  a,  and  join  a with  b and  x. 


The  height  k e of  the  ridge  of  the  dormer  roof  is  known,  and 
we  must  find  where  this  ridge  will  meet  the  main  roof.  The  ridge 
must  be  a 30°  line  as  it  runs  parallel  to  the  end  wall  of  the  house 


131 


44 


MECHANICAL  DRAWING 


and  to  the  ground.  Draw  from  e d line  parallel  to  b h to  meet  a 
vertical  through  h at  f This  point  is  in  the  vertical  plane  of  the 
end  wall  of  the  house,  hence  in  the  plane  of  i Ti.  If  now  a 80°  line 
be  drawn  from  f parallel  to  x b , it  will  meet  the  roof  of  the  house 
at  g.  The  dormer  ridge  and  f g are  in  the  same  horizontal  plane, 
hence  will  meet  the  roof  at  the  same  distance  below  the  ridge  a i. 
Therefore  draw  the  80°  line  g c,  and  connect  c with  d. 

In  Fig.  58  a box  is  shown  with  the  cover  opened  through  150°. 


The  right-hand  edge  of  the  bottom  shows  the  width,  the  left-hand 
edge  the  length,  and  the  vertical  edge  the  height.  The  short  edges 
of  the  cover  are  not  isometric  lines,  hence  are  not  shown  in  their 
true  lengths;  neither  is  the  angle  through  which  the  cover  is  opened 
represented  in  its  actual  size. 

The  corners  of  the  cover  must  then  be  determined  by  co- 
ordinates from  an  end  view  of  the  box  and  cover.  As  the  end  of 
the  cover  is  in  the  same  plane  as  the  end  of  the  box,  the  simple 


132 


MECHANICAL  DRAWING 


45 


end  view  as  shown  in  Fig.  59  will  be  sufficient.  Extend  the  top  of 
the  box  to  the  right,  and  from  c and  d let  fall  perpendiculars  or 
a b produced,  giving  the  points  e and  f.  The  point  c may  be 
located  by  means  of  the  two  distances  or  co-ordinates  b e and  e c. 


and  these  distances  will  appear  in  their  true  lengths  in  the 
isometric  view.  Hence  produce  a ' br  to  e ' and  f' ; and  from  these 
points  draw  verticals  er  c'  and f'  d’ ; make  b'  e'  equal  to  b e,  e'  c' 
equal  to  e c;  and  similarly  for  d' . Draw  the  lower  edge  parallel 
to  c'  d'  and  equal  to  it  in  length,  and 
connect  with  b ' . 

It  will  be  seen  that  in  isometric  draw- 
ing parallel  lines  always  appear  parallel. 

It  is  also  true  that  lines  divided  propor- 
tionally maintain  this  same  relation  in 
isometric  drawing. 

Fig.  60  shows  a block  or  prism  with  a 
semicircular  top.  Find  the  isometric  of 
the  square  circumscribing  the  circle,  then 
draw  the  curve  by  the  approximate  method. 

The  centers  for  the  back  face  are  found 
by  projecting  the  front  centers  back  30° 
equal  to  the  thickness  of  the  prism,  as 
shown  at  a and  b.  The  plan  and  elevation  of  an  oblique  pentagonal 
pyramid  are  shown  in  Fig.  61.  It  is  evident  that  none  of  the 
edges  of  the  pyramid  can  be  drawn  in  isometric  as  either  vertical 
or  30°  lines;  hence,  a system  of  co-ordinates  must  be  used  as 


Fig.  60. 


133 


46 


MECHANICAL  DRAWING 


shown  in  Fig.  58.  This  problem  illustrates  the  most  general  case; 
and  to  locate  some  of  the  points  three  co-ordinates  must  be  used, 
two  at  80°  and  one  vertical. 

Circumscribe,  about  the  plan  of  the  pyramid,  a rectangle  which 
shall  have  its  sides  respectively  parallel  and  perpendicular  to  the 
ground  line.  This  rectangle  is  on  H,  and  its  vertical  projection  is 
in  the  ground  line. 

The  isometric  of  this  rectangle  can  be  drawn  at  once  with  30° 
lines,  as  shown  in  Fig.  62,  o being  the  same  point  in  both  figures. 


Fig.  61. 


The  horizontal  projection  of  point  8 is  found  in  isometric  at  3h,  at 
the  same  distance  from  o as  in  the  plan.  That  is,  any  distance 
which  in  plan  is  parallel  to  a side  of  the  circumscribing  rectangle, 
is  shown  in  isometric  in  its  true  length  and  parallel  to  the  corre- 
sponding side  of  the  isometric  rectangle . If  point  3 were  on  the 
horizontal  plane  its  isometric  would  be  3h,  but  the  point  is  at  the 
vertical  height  above  H given  in  the  elevation ; hence,  lay  off  above 
3h  this  vertical  height,  obtaining  the  actual  isometric  of  the  point. 
To  locate  4,  draw  4 a parallel  to  the  side  of  the  rectangle;  then  lay 


134 


MECHANICAL  DRAWING 


47 


off  o a and  a 4h,  giving  what  may  be  called  the  isometric  plan  of  4. 
Next,  the  vertical  height  taken  from  the  elevation  locates  the  iso- 
metric of  the  point  in  space. 

In  like  manner  all  the 
corners  of  the  pyramid,  in- 
cluding the  apex,  are  located. 

The  rule  is,  locate  first  in 
isometric  the  horizontal  pro- 
jection of  a point  by  one  or 
two  30°  co-ordinates ; then 
vertically,  above  this  point, 
its  height  as  taken  from 
the  elevation.  The  shade 
lines  cannot  be  determined 
here  by  applying  the  30°  or 
60°  triangle,  owing  to  the 
obliquity  of  the  faces.  Since 
the  right  front  corner  of  the 
rectangle  in  plan  was  made  the  point  o in  isometric,  the  shade 
lines  must  be  the  same  in  isometric  as  in  actual  projection;  so  that, 

if  these  can  be  de- 
termined in  Fig.  61, 
they  may  be  applied 
at  once  to  Fig.  62. 

The  shade  lines 
in  Fig.  61  are  found 
by  a short  method 
which  is  convenient 
to  use  when  the  exact 
shade  lines  are  de- 
sired, and  when  they 
cannot  be  deter- 
mined by  applying 
the  45°  triangle.  A 
plane  is  taken  at  45° 
with  the  horizontal 
plane,  and  parallel  to  the  direction  of  the  ray  of  light,  in  such  a 
position  as  to  cut  all  the  surfaces  of  the  pyramid,  as  shown  in 


135 


48 


MECHANICAL  DRAWING 


elevation.  This  plane  is  perpendicular  to  the  vertical  plane;  hence 
the  section  it  cuts  from  the  pyramid  is  readily  found  in  plan  by 
projection.  This  plane  contains  some  of  the  rays  of  light  falling 
upon  the  pyramid;  and  we  can  tell  what  surfaces  these  rays  strike 


and  make  light,  by  noticing  on  the  plan  what  edges  of  the  section  are 
struck  by  the  projections  of  the  rays  of  light.  That  is,  rs,st,  and  t u 
receive  the  rays  of  light;  hence  the  surfaces  on  which  these  lines  lie 
are  light,  r s is  on  the  surface  determined  by  the  two  lines  passing 


136 


MECHANICAL  DRAWING 


49 


through  r and  s,  namely,  2—1  and  1 — 5;  in  other  words,  r s is 
on  the  base;  similarly,  s t is  on  the  surface  1 — 5 — 6;  and  t u on 
the  surface  4 — 6 — 5.  The  other  surfaces  are  dark ; hence  the  edges 
which  are  between  the  light  and  dark  faces  are  the  shade  lines. 

Whenever  it  is  more  convenient,  a plane  parallel  to  the  ray 
of  light  and  perpendicular  to  H may  be  taken,  the  section  found 
in  elevation,  and  the  45°  triangle  applied  to  this  section.  The 
same  method  may  be  used  to  determine  the  exact  shade  lines 
of  a cone  or  cylinder  in  an  oblique  position. 

Figs.  63  to  70  give  examples  of  the  isometric  of  various 
objects.  Fig.  65  is  the  plan  and  elevation,  and  Fig.  66  the 


Fig.  69.  Fig.  70. 


isometric,  of  a carpenter’s  bench.  In  Fig.  70,  take  especial  notice 
of  the  shade  lines.  These  are  put  on  as  if  the  group  were  made 
in  one  piece ; and  the  shadows  cast  by  the  blocks  on  one  another 
are  disregarded.  All  upper  horizontal  faces  are  light,  all  left-hand 
(front  and  back)  faces  light,  and  the  rest  dark. 

OBLIQUE  PROJECTIONS. 

In  oblique  projection,  as  in  isometric,  the  end  sought  for  is 
the  same — a more  or  less  complete  representation,  in  one  view,  of 
any  object.  Oblique  projection  differs  from  isometric  in  that  one 
face  of  the  object  is  represented  as  if  parallel  to  the  vertical 
plane  of  projection,  the  others  inclined  to  it.  Another  point  of 


137 


50 


MECHANICAL  DRAWING 


difference  is  that  oblique  projection  cannot  be  deduced  from 
orthographic  projection,  as  is  isometric. 

In  oblique  projection  all  lines  in  the  front  face  are  shown  in 
their  true  lengths  and  in  their  true  relation  to  one  another,  and 
lines  which  are  perpendicular  to  this  front  face  are  shown  in  their 
true  lengths  at  any  angle  that  may  be  desired  for  any  particular 
case.  Lines  not  in  the  plane  of  the  front  face  nor  perpendicular 


to  it  must  be  determined  by  co-ordinates,  as  in  isometric.  It  will 
be  seen  at  once  that  this  system  possesses  some  advantages  over 
the  isometric,  as,  for  instance,  in  the  representation  of  circles, 


as  any  circle  or  curve  in  the  front  face  is  actually  drawn  as  such. 

The  rays  of  light  are  still  supposed  to  be  parallel  to  the  same 
diagonal  of  the  cube,  that  is,  sloping  downward,  toward  the  plane 
of  projection,  and  to  the  right,  or  downward,  backward  and  to 
the  right.  Figs.  71,  72  and  73  show  a cube  in  oblique  projection, 


138 


MECHANICAL  DRAWING 


51 


with  the  30°,  45°  and  60°  slant  respectively.  The  dotted  diagonal 
represents  for  each  case  the  direction  of  the  light,  and  the  shade 
lines  follow  from  this. 

The  shade  lines  have  the  same  general  position  as  in  isometric 


drawing,  the  top,  front  and  left-hand  faces  being  light.  No  matter 
what  angle  may  be  used  for  the  edges  that  are  perpendicular  to 
the  front  face,  the  £>rojection  Qf  the  diagonal  of  the  cube  on  this 
face  is  always  a 45°  line;  hence,  for  determining  the  shade  lines  on 


any  front  face,  such  as  the  end  of  the  hollow  cylinder  in  Fig.  74, 
the  45°  line  is  used  exactly  as  in  the  elevation  of  ordinary 
projections. 

Figs.  75,  76,  77  and  79  are  other  examples  of  oblique  projections. 
Fig.  77  is  a crank  arm. 

The  method  of  using  co-ordinates  for  lines  of  which  the  true 


139 


52 


MECHANICAL  DRAWING 


lengths  are  not  shown,  is  illustrated  by  Figs.  78  and  79.  Fig.  79 
represents  the  oblique  projection  of  the  two  joists  shown  in  plan 
and  elevation  in  Fig.  78.  The  dotted  lines  in  the  elevation  (see 
Fig.  78)  show  the  heights  of  the  corners  above  the  horizontal 
stick.  The  feet  of  these  perpendiculars  give  the  horizontal  dis- 
tances of  the  top  corners  from  the  end  of  the  horizontal  piece. 

In  Fig.  79  lay  off  from  the  upper  right-hand  corner  of  the 
front  end  a distance  equal  to  the  distance  between  the  front  edge 
of  the  inclined  piece  and  the  front  edge  of  the  bottom  piece  (see 
Fig.  78).  From  this  point  draw  a dotted  line  parallel  to  the 


Fig.  78. 

length.  The  horizontal  distances  from  the  upper  left  corner  to 
the  dotted  perpendicular  are  then  marked  off  on  this  line.  From 
these  points  verticals  are  drawn,  and  made  equal  in  length  to  the 
dotted  perpendiculars  of  Fig.  78,  thus  locating  two  corners  of  the 
end. 

LINE  SHADING. 

In  finely  finished  drawings  it  is  frequently  desirable  to  make 
the  various  parts  more  readily  seen  by  showing  the  graduations  of 
light  and  shade  on  the  curved  surfaces.  This  is  especially  true  of 
such  surfaces  as  cylinders,  cones  and  spheres.  The  effect  is 
obtained  by  drawing  a series  of  parallel  or  converging  lines  on 
the  surface  at  varying  distances  from  one  another.  Sometimes 
draftsmen  vary  the  width  of  the  lines  themselves.  These  lines  are 
farther  apart  on  the  lighter  portion  of  the  surface,  and  are  closer 
together  and  heavier  on  the  darker  part. 


140 


MECHANICAL  DRAWING 


53 


Fig.  80  shows  a cylinder  with  elements  drawn  on  the  surface 
equally  spaced,  as  on  the  plan.  On  account  of  the  curvature  of 
the  surface  the  elements  are  not  equally  spaced  on  the  elevation, 
but  give  the  effect  of  graduation  of  light.  The 
result  is  that  in  elevation  the  distances  between 
the  elements  gradually  lessen  from  the  center 
toward  each  side,  thus  showing  that  the  cylinder 
is  convex.  The  effect  is  intensified,  however,  if 
the  elements  are  made  heavier,  as  well  as  closer 
together,  as  shown  in  Figs.  81  to  87. 

Cylinders  are  often  shaded  with  the  light 
coming  in  the  usual  way,  the  darkest  part  com- 
mencing about  where  the  shade  line  would  actually 
be  on  the  surface,  and  the  lightest  portion  a little 
to  the  left  of  the  center.  Fig.  81  is  a cylinder 
showing  the  heaviest  shade  at  the  right,  as  this 
method  is  often  used.  Considerable  practice  is 
necessary  in  order  to  obtain  good  results;  but  in 
this,  as  in  other  portions  of  mechanical  drawing, 
perseverance  has  its  reward.  Fig.  82  represents  a cylinder  in  a 
horizontal  position,  and  Fig.  83  represents  a section  of  a hollow 
vertical  cylinder. 


Fig.  81. 


Fig.  82. 


Fig.  83. 


Figs.  84  to  87  give  other  examples  of  familiar  objects. 

In  the  elevation  of  the  cone  shown  in  Fig.  87  the  shade  lines 
should  diminish  in  weight  as  they  approach  the  apex.  Unless 
this  is  done  it  will  be  difficult  to  avoid  the  formation  of  a blot  at 
that  point. 


141 


54 


MECHANICAL  DRAWING 


LETTERING. 

All  working  drawings  require  more  or  less  lettering,  such  as 
titles,  dimensions,  explanations,  etc.  In  order  that  the  drawing 
may  appear  finished,  the  lettering  must  be  well  done.  No  style 
of  lettering  should  ever  be  used  which  is  not  perfectly  legible. 
It  is  generally  best  to  use  plain,  easily-made  letters  which  present 


Fig.  84. 


Fig.  85. 


a neat  appearance.  Small  letters  used  on  the  drawing  for  notes  or 
directions  should  be  made  free-hand  with  an  ordinary  waiting  pen. 
Two  horizontal  guide  lines  should  be  used  to  limit  the  height  of 
the  letters;  after  a time,  however,  the  upper  guide  line  may  be 
omitted. 


142 


mechanical  drawing 


00 


In  the  early  part  of  this  course  the  inclined  Gothic  letter  was 
described,  and  the  alphabet  given.  The  Roman,  Gothic  and  block 
letters  are  perhaps  the  most  used  for  titles.  These  letters,  being 
of  comparatively  large  size,  are  generally  made  mechanically;  that 
is,  drawing  instruments  are  used  in  their  construction.  In  order 
that  the  letters  may  appear  of  the  same  height,  some  of  them, 
owing  to  their  shape,  must  be  made  a little  higher  than  the  others. 
This  is  the  case  with  the  letters  curved  at  the  top  and  bottom, 
such  as  C,  O,  S,  etc.,  as  shown  somewhat  exaggerated  in 
Fig.  88.  Also,  the  letter  A should  extend  a little  above,  and  V a 
little  below,  the  guide  lines,  because  if  made  of  the  same  height 
as  the  others  they  will  appear  shorter.  This  is  true  of  all  capitals, 
whether  of  Roman,  Gothic,  or  other  alphabets.  In  the  block  letter, 
however,  they  are  frequently  all  of  the  same  size. 

There  is  no  absolute  size  or  proportion  of  letters,  as  the 
dimensions  are  regulated  by  the  amount  of  sj)ace  in  which  the 
letters  are  to  be  placed,  the  size  of  the  drawing,  the  effect  desired, 
etc.  In  some  cases  letters  are  made  so  that  the  height  is  greater 
than  the  width,  and  sometimes  the  reverse;  sometimes  the  height 
and  width  are  the  saipe.  This  last  proportion  is  the  most  common. 
Certain  relations  of  width,  however,  should  be  observed.  Thus,  in 
whatever  style  of  alphabet  used,  the  W should  be  the  widest  letter; 
J the  narrowest,  M and  T next  widest  to  W,  then  A and  B.  The 
other  letters  are  of  about  the  same  width. 

In  the  vertical  Gothic  alphabet,  the  average  height  is  that  of 
B.  D.  E,  F,  etc.,  and  the  additional  height  of  the  curved  letters 
and  of  the  A and  V is  very  slight.  The  horizontal  cross  lines  of 
such  letters  as  E.  F.  H.  etc.,  are  slightly  above  the  center;  those 
of  A,  G and  P slightly  below. 

For  the  inclined  letters,  60°  is  a convenient  angle,  although 
they  may  be  at  any  other  angle  suited  to  the  convenience  or  fancy 
of  the  draftsman.  Many  draftsmen  use  an  angle  of  about  70°. 

The  letters  of  the  Roman  alphabet,  whether  vertical  or 
inclined,  are  quite  ornamental  in  effect  if  well  made,  the  inclined 
Roman  being  a particularly  attractive  letter,  although  rather 
difficult  to  make.  The  block  letter  is  made  on  the  same  general 
plan  as  the  Gothic,  but  much  heavier.  Small  squares  are  taken  as 


143 


56 


MECHANICAL  DRAWING. 


u 


Inclined  Gothic  Capitals. 


MECHANICAL  DRAWING 


57 


the  unit  of  measurement,  as  shown.  The  use  of  this  letter  is  not 
advocated  for  general  work,  although  if  made  merely  in  outline  the 
effect  is  pleasing.  The  styles  of  numbers  corresponding  with 
the  alphabets  of  capitals  given  here,  are  also  inserted.  When  a 
fraction,  such  as  2§  is  to  be  made,  the  proportion  should  be  about 
as  shown.  For  small  letters,  usually  called  lower-case  letters, 

abcdefghijklmn 

opqrstuvwxyz 

Fig.  89. 

obcc/efgh/jk/mn 
opqrs  tuv  wyyz 

Fig.  90. 

abcdefghijklmn 

opqrstuvwxyz 

Fig.  91. 

» 

the  height  may  be  made  about  two-thirds  that  of  the  capitals. 
This  proportion,  however,  varies  in  special  cases. 

The  principal  lower-case  letters  in  general  use  among  drafts- 
men are  shown  in  Figs.  89,  90,  91  and  92.  The  Gothic  letters 
shown  in  Figs.  89  and  90  are  much  easier  to  make  than  the 
Roman  letters  in  Figs.  91  and  92.  These  letters,  however,  do  not 


145 


AB  C D E F G HI  JKLMN 


58 


MECHANICAL  DRAWING. 


Inclined  Homan  Capitals. 


MECHANICAL  DRAWING 


59 


give  as  finished  an  appearance  as  the  Roman.  As  has  already 
been  stated  in  Mechanical  Drawing,  Part  I,  the  inclined  letter  is 
easier  to  make  because  slight  errors  are  not  so  apparent. 

One  of  the  most  important  points  to  be  remembered  in  letter- 
ing is  the  spacing.  If  the  letters  are  finely  executed  but  poorly 
spaced,  the  effect  is  not  good.  To  space  letters  correctly  and 
rapidly,  requires  considerable  experience;  and  rules  are  of  little 
value  on  account  of  the  many  combinations  in  which  letters  are 

abode  fg  hijklmn 
opqrs  tuvwxy  z 

Fig.  92. 

found.  A few  directions,  however,  may  be  found  helpful.  For 
instance,  take  the  word  TECHNICALITY,  Fig.  93.  If  all  the 
spaces  were  made  equal,  the  space  between  the  L and  the  I would 
appear  to  be  too  great,  and  the  same  would  apply  to  the  space 
between  the  I and  the  T.  The  space  between  the  H and  the  _N 
and  that  between  the  N and  the  I would  be  insufficient.  In 
general,  when  the  vertical  side  of  one  letter  is  followed  by  the  verti- 
cal side  of  another,  as  in  H E,  H B,  I R,  etc.,  the  maximum  space 

TECHNICALITY 

Fig.  93. 

should  be  allowed.  Where  T and  A come  together  the  least  space 
is  given,  for  in  this  case  the  top  of  the  T frequently  extends  over 
the  bottom  of  the  A.  In  general,  the  spacing  should  be  such  that 
a uniform  appearance  is  obtained.  For  the  distances  between 
words  in  a sentence,  a space  of  about  1^  the  width  of  the  average 
letter  may  be  used.  The  space,  however,  depends  largely  upon  the 
desired  effect. 


147 


60 


MECHANICAL  DRAWING 


For  large  titles,  such  as  those  placed  on  charts,  maps,  and 
some  large  working  drawings,  the  letters  should  be  penciled  before 
inking.  If  the  height  is  made  equal  to  the  wTidth  considerable 
time  and  labor  will  be  saved  in  laying  out  the  wx>rk.  This  is 
especially  true  with  such  Gothic  letters  as  O,  Q,  C,  etc.,  as  these 
letters  may  then  be  made  with  compasses.  If  the  letters  are  of 
sufficient  size,  the  outlines  may  be  drawn  with  the  ruling  pen  or 
compasses,  and  the  spaces  between  filled  in  with  a fine  brush. 

The  titles  for  working  drawings  are  generally  placed  in  the 
lower  right-hand  corner.  Usually  a draftsman  has  his  choice  of 


Block  Letters. 


letters,  mainly  because  after  he  has  become  used  to  making  one 
style  he  can  do  it  rapidly  and  accurately.  However,  in  some  draft- 
ing rooms  the  head  draftsman  decides  what  lettering  shall  be  used. 
In  making  these  titles,  the  different  alphabets  are  selected  to  give 
the  best  results  without  spending  too  much  time.  In  most  work 
the  letters  are  made  in  straight  lines,  although  we  frequently  find 
a portion  of  the  title  lettered  on  an  arc  of  a circle. 

In  Fig.  94  is  shown  a title  having  the  words  CONNECTING 
ROD  lettered  on  an  arc  of  a circle.  To  do  this  work  requires 
considerable  patience  and  practice.  First  draw  the  vertical  center 


148 


MECHANICAL  DRAWING 


61 


line  as  shown  at  C in  Fig.  94.  Then  draw  horizontal  lines  for  the 
horizontal  letters.  The  radii  of  the  arcs  depend  upon  the  general 
arrangement  of  the  entire  title,  and  this  is  a matter  of  taste.  The 
difference  between  the  arcs  should  equal  the  height  of  the  letters. 
After  the  arc  is  drawn,  the  letters  should  be  sketched  in  pencil  to 
find  their  approximate  positions.  After  this  is  done,  draw  radial 
lines  from  the  center  of  the  letters  to  the  center  of  the  arcs. 


BEAM  ENGINE 

SCALE  3 INCHES  = 1 FOOT 


PORTLAND  COMPANY’S  WORKS 

JULY  10,  1894 

F'ig.  94. 


These  lines  will  be  the  centers  of  the  letters,  as  shown  at  A,  B,  D 
and  E.  The  vertical  lines  of  the  letters  should  not  radiate  from 
the  center  of  the  arc,  but  should  be  parallel  to  the  center  lines 
already  drawn;  otherwise  the  letters  will  appear  distorted.  Thus, 
in  the  letter  N the  two  verticals  are  parallel  to  the  line  A.  The 
same  applies  to  the  other  letters  in  the  alphabet. 


149 


62 


. MECHANICAL  DRAWING 


Tracing.  Having  finished  the  pencil  drawing,  the  next  step 
is  the  inking.  In  some  offices  the  pencil  drawing  is  made  on  a thin, 
tough  paper,  called  board  paper,  and  the  inking  is  done  over  the 
pencil  drawing,  in  the  manner  with  wdiich  the  student  is  already 
familiar.  It  is  more  common  to  do  the  inking  on  thin,  trans- 
parent  cloth,  called  tracing  cloth,  which  is  prepared  for  the  pur- 
pose.  This  tracing  cloth  is  made  of  various  kinds,  the  kind  in 
ordinary  use  being  what  is  known  as  “ dull  back,”  that  is,  one 
side  is  finished  and  the  other  side  is  left  dull.  Either  side  may 
be  used  to  draw  upon,  but  most  draftsmen  prefer  the  dull  side. 
If  a drawing  is  to  be  traced  it  is  a good  plan  to  use  a 3H  or  411 
pencil,  so  that  the  lines  may  be  easily  seen  through  the  cloth. 

The  tracing  cloth  is  stretched  smoothly  over  the  pencil  draw- 
ing and  a little  powdered  chalk  rubbed  over  it  with  a dry  cloth, 
to  remove  the  slight  amount  of  grease  or  oil  from  the  surface  and 
make  it  take  the  ink  better.  The  dust  must  be  carefully  brushed 
or  wiped  off  with  a soft  cloth,  after  the  rubbing,  or  it  will  inter- 
fere with  the  inking. 

The  drawing  is  then  made  in  ink  on  the  tracing  cloth,  after 
the  same  general  rules  as  for  inking  the  paper,  but  care  must  be 
taken  to  draw  the  ink  lines  exactly  over  the  pencil  lines  which 
are  on  the  paper  underneath,  and  which  should  be  just  heavy 
enough  to  be  easily  seen  through  the  tracing  cloth.  The  ink  lines 
should  be  firm  and  fully  as  heavy  as  for  ordinary  work.  In  tracing, 
it  is  better  to  complete  one  view  at  a time,  because  if  parts  of 
several  views  are  traced  and  the  drawing  left  for  a day  or  two,  the 
cloth  is  liable  to  stretch  and  warp  so  that  it  will  be  difficult  to 
complete  the  views  and  make  the  new  lines  fit  those  already 
drawn  and  at  the  same  time  conform  to  the  pencil  lines  under- 
neath. For  this  reason  it  is  well,  when  possible,  to  complete  a 
view  before  leaving  the  drawing  for  any  length  of  time,  although 
of  course  on  views  in  which  there  is  a good  deal  of  work  this 
cannot  always  be  done.  In  this  case  the  draftsman  must  manipu- 
late his  tracing;  cloth  and  instruments  to  make  the  lines  fit  as  best 
he  can.  A skillful  draftsman  will  have  no  trouble  from  this 
source,  but  the  beginner  may  at  first  find  difficulty. 

Inking  on  tracing  cloth  will  be  found  by  the  beginner  to  be 
quite  different  from  inking  on  the  paper  to  which  he  has  been 
accustomed,  and  he  will  doubtless  make  many  blots  and  think  at 


150 


TYPICAL  ARCHITECT’S  DRAWING  SHOWING  DETAILS  OF  WINDOW  FRAME. 


MECHANICAL  DRAWING 


63 


first  that  it  is  hard  to  make  a tracing.  After  a little  practice, 
however,  he  will  find  that  the  tracing  cloth  is  very  satisfactory 
and  that  a good  drawing  can  be  made  on  it  quite  as  easily  as  on 
paper. 

The  necessity  for  making  erasures  should  be  avoided,  as  far 
as  possible,  but  when  an  erasure  must  be  made  a good  ink  rubber 
or  typewriter  eraser  may  be  used.  If  the  erased  line  is  to  have 
ink  placed  on  it,  such  as  a line  crossing,  it  is  better  to  use  a soft 
rubber  eraser.  All  moisture  should  be  kept  from  the  cloth. 

Blue  Printing,  The  tracing,  of  course,  cannot  be  sent  into 
the  shop  for  the  workmen  to  use,  as  it  would  soon  become  soiled 
and  in  time  destroyed,  so  that  it  is  necessary  to  have  some  cheap 
and  rapid  means  of  making  copies  from  it.  These  copies  are 
made  by  the  process  of  blue  printing  in  wThich  the  tracing  is  used 
in  a manner  similar  to  the  use  made  of  a negative  in  photography. 

Almost  all  drafting  rooms  have  a frame  for  the  purpose  of 
making  blue  prints.  These  frames  are  made  in  many  styles,  some 
simple,  some  elaborate.  A simple  and  efficient  form  is  a flat  sur- 
face usually  of  wood,  covered  with  padding  of  soft  material,  such 
as  felting.  To  this  is  hinged  the  cover,  which  consists  of  a frame 
similar  to  a picture  frame,  in  which  is  set  a piece  of  clear  glass. 
The  whole  is  either  mounted  on  a track  or  on  some  sort  of  a 
swinging  arm,  so  that  it  may  readily  be  run  in  and  out  of  a 
window. 

The  print  is  made  on  paper  prepared  for  the  purpose  by 
having  one  of  its  surfaces  coated  with  chemicals  which  are  sensi- 
tive to  sunlight.  This  coated  paper,  or  blue-print  paper,  as  it  is 
called,  is  laid  on  the  padded  surface  of  the  frame  with  its  coated 
side  uppermost;  the  tracing  laid  over  it  right  side  up,  and  the 
glass  pressed  down  firmly  and  fastened  in  place.  Springs  are 
frequently  used  to  keep  the  paper,  tracing,  etc.,  against  the  glassy 
With  some  frames  it  is  more  convenient  to  turn  them  over  and 
remove  the  backs.  In  such  cases  the  tracing  is  laid  against  the 
glass,  face  down;  the  coated  paper  is  then  placed  on  it  with  the 
coated  side  against  the  tracing  cloth. 

The  sun  is  allowed  to  shine  upon  the  drawing  for  a few 
minutes,  then  the  blue-print  paper  is  taken  out  and  thoroughly 
washed  in  clean  water  for  several  minutes  and  hung  up  to  dry. 


153 


(54 


MECHANICAL  DRAWING 


If  the  paper  has  been  recently  prepared  and  the  exposure  properly 
timed,  the  coated  surface  of  the  paper  will  now  be  of  a clear,  deep 
blue  color,  except  where  it  was  covered  by  the  ink  lines,  where  it 
will  be  perfectly  white. 

The  action  has  been  this:  Before  the  paper  was  exposed  to 

the  light  the  coating  was  of  a pale  yellow  color,  and  if  it  had  then 
been  put  in  water  the  coating  would  have  all  washed  off,  leaving 
the  paper  white.  In  other  words,  before  being  exposed  to  the 
sunlight  the  coating  was  soluble.  The  light  penetrated  the  trans- 
parent tracing  cloth  and  acted  upon  the  chemicals  of  the  coating, 
changing  their  nature  so  that  they  became  insoluble;  that  is,  when 
put  in  water,  the  coating,  instead  of  being  washed  off,  merely 
turned  blue.  The  light  could  not  penetrate  the  ink  with  which 
the  lines,  figures,  etc.,  were  drawn,  consequently  the  coating  under 
these  was  not  acted  upon  and  it  washed  off  when  put  in  water, 
leaving  a white  copy  of  the  ink  drawing  on  a blue  background. 
If  running  water  cannot  be  used,  the  paper  must  be  washed  in  a 
sufficient  number  of  changes  until  the  water  is  clear.  It  is  a good 
plan  to  arrange  a tank  having  an  overflow,  so  that  the  water  may 
remain  at  a depth  of  about  6 or  8 inches. 

The  length  of  time  to  which  a print  should  be  exposed  to  the 
light  depends  upon  the  quality  and  freshness  of  the  paper,  the 
chemicals  used  and  the  brightness  of  the  light.  Some  paper  is 
prepared  so  that  an  exposure  of  one  minute,  or  even  less,  in  bright 
sunlight,  will  give  a good  print  and  the  time  ranges  from  this  to 
twenty  minutes  or  more,  according  to  the  proportions  of  the 
various  chemicals  in  the  coating.  If  the  full  strength  of  the  sun- 
light does  not  strike  the  paper,  as,  for  instance,  if  clouds  partly 
cover  the  sun,  the  time  of  exposure  must  be  lengthened. 

Assembly  Drawing.  We  have  followed  through  the  process 
of  making  a detail  drawing  from  the  sketches  to  the  blue  print 
ready  for  the  workmen.  Such  a detail  drawing  or  set  of  drawings 
shows  the  form  and  size  of  each  piece,  but  does  not  show  how  the 
pieces  go  together  and  gives  no  idea  of  the  machine  as  a whole. 
Consequently,  a general  drawing  or  assembly  drawing  must  be 
made,  which  will  show  these  things.  Usually  two  or  more  views 
are  necessary,  the  number  depending  upon  the  complexity  of  the 
machine.  Very  often  a cross-section  through  some  part  of  the 


154 


MECHANICAL  DRAWING 


G5 


machine,  chosen  so  as  to  give  the  best  general  idea  with  the  least 
amount  of  work,  will  make  the  drawing-  clearer. 

The  number  of  dimensions  required  on  an  assembly  drawing 
depends  largely  upon  the  kind  of  machine.  It  is  usually  best  to 
give  the  important  over-all  dimensions  and  the  distance  between 
the  principal  center  lines.  Care  must  be  taken  that  the  over-all 
dimensions  agree  with  the  sum  of  the  dimensions  of  the  various 
details.  For  example,  suppose  three  pieces  are  bolted  together, 
the  thickness  of  the  pieces  according  to  the  detail  drawing,  being 
one  inch,  two  inches,  and  five  and  one-half  inches  respectively;  the 
sum  of  these  three  dimensions  is  eight  and  one -half  inches  and 
the  dimensions  from  outside  on  the  assembly  drawing,  if  given  at 
all,  must  agree  with  this.  It  is  a good  plan  to  add  these  over-all 
dimensions,  as  it  serves  as  a check  and  relieves  the  mechanic  of  the 
necessity  of  adding  fractions. 

FORMULA  FOR  BLUE=PRINT  SOLUTION. 

Dissolve  thoroughly  and  filter. 


Red  Prussiate  of  potash * 2*4  ounces, 

Water . . ...o....  1 pint, 

Ammonio-Citrate  of  iron 4 ounces, 

B'  Water , . 1 pint. 

Use  equal  parts  of  A and  B. 


FORHULA  FOR  BLACK  PRINTS 

Negatives.  White  lines  on  blue  ground;  prepare  the  paper 


with 

Ammonio-Citrate  of  iron.  . 40  grains, 

Water 1 ounce. 


After  printing  wash  in  water. 

Positives.  Black  lines  on  white  ground;  prepare  the  paper 


with: 

Iron  perchloride 616  grains, 

Oxalic  Acid 308  grains, 

Water 14  ounces. 

T Gallic  Acid. 1 ounce, 

Develop  in  1 Citric  Acid 1 ounce, 

( Alum 8 ounces. 


Use  1^  ounces  of  developer  to  one  gallon  of  water.  Paper  is 
fully  exposed  when  it  has  changed  from  yellow  to  white. 


155 


66 


MECHANICAL  DRAWING 


PLATES. 

PLATE  SX. 

The  plates  of  this  Instruction. Paper  should  be  laid  out  at  the 
same  size  as  the  plates  in  Parts  I and  II.  The  center  lines  and 
border  lines  should  also  be  drawn  as  described. 

First  draw  two  ground  lines  across  the  sheet,  3 inches  below 
the  upper  border  line  and  3 inches  above  the  lower  border  line. 
The  first  problem  on  each  ground  line  is  to  be  placed  1 inch  from 
the  left  border  line;  and  spaces  of  about  1 inch  should  be  left 
between  the  figures. 

Isolated  points  are  indicated  by  a small  cross  X,  and  projections 
of  lines  are  to  be  drawn  full  unless  invisible.  All  construction 
lines  should  be  fine  dotted  lines.  Given  and  required  lines  should 
be  drawn  full. 

Problems  on  Upper  Ground  Line: 

1.  Locate  both  projections  of  a point  on  the  horizontal  plane 
1 inch  from  the  vertical  plane. 

2.  Draw  the  projections  of  a line  2 inches  long  which  is 
parallel  to  the  vertical  plane  and  which  makes  an  angle  of  45 
degrees  with  the  horizontal  plane  and  slants  upward  to  the  right. 

The  line  should  be  1 inch  from  the  vertical  plane  and  the  lower  end 
inch  above  the  horizontal. 

3 Draw  the  projections  of  a line  1J  inches  long  which  is 
parallel  to  both  planes,  1 inch  above  the  horizontal,  and  f inch  from 
the  vertical. 

4.  Draw  the  plan  and  elevation  of  a line  2 incnes  long  which 
is  parallel  to  H and  makes  an  angle  of  30  degrees  with  V.  Let  the 
right-hand  end  of  the  line  be  the  end  nearer  V,  ^ inch  from  V. 
The  line  to  be  1 inch  above  H. 

5.  Draw  the  plan  and  elevation  of  a line  1^  inches  long 
which  is  perpendicular  to  the  horizontal  plane  and  1 inch  from  the 
vertical.  Lower  end  of  line  is  \ inch  above  H. 

6.  Draw  the  projections  of  a line  1 inch  long  which  is 
perpendicular  to  the  vertical  plane  and  1^  inches  above  the 
horizontal.  The  end  of  the  lino  nearer  V,  or  the  back  end,  is 
| inch  from  V. 


156 


EEBRUARY  /7,  190/.  HERBERT  CHANDLER , CH/CAGO,  ILL. 


ELATE 


MECHANICAL  DRAWING 


G7 


7.  Draw  two  projections  which  shall  represent  a line  oblique 
to  both  planes. 

Note.  Leave  1 inch  between  this  figure  and  the  right-hand  border  line. 

Problems  on  Lower  Ground  Line : 

8.  Draw  the  projections  of  two  parallel  lines  each  1-J  inches 
long.  The  lines  are  to  be  parallel  to  the  vertical  plane  and  to  make 
angles  of  GO  degrees  with  the  horizontal.  The  lower  end  of  each 
line  is  \ inch  above  H.  The  right-hand  end  of  the  right-hand  line 
is  to  be  2f  inches  from  the  left-hand  margin. 

9.  Draw  the  projections  of  two  parallel  lines  each  2 inches 
long.  Both  lines  to  be  parallel  to  the  horizontal  and  to  make 
an  angle  of  30  degrees  with  the  vertical.  The  lower  line  to  be 
§ inch  above  H,  and  one  end  of  one  line  to  be  against  V. 

10.  Draw  the  projections  of  two  intersecting  lines.  One 
2 inches  long  to  be  parallel  to  both  planes,  1 inch  above  H,  and 
f inch  from  the  vertical;  and  the  other  to  be  oblique  to  both 
planes  and  of  any  desired  length. 

11.  Draw  plan  and  elevation  of  a prism  1 inch  square  and  1| 
inches  long.  The  prism  to  have  one  side  on  the  horizontal  plane, 
and  its  long  edges  to  be  perpendicular  to  V.  The  back  end  of  the 
prism  is  J inch  from  the  vertical  plane. 

12.  Draw  plan  and  elevation  of  a prism  the  same  size  as  given 
above,  but  with  the  long  edges  parallel  to  both  planes,  the  lower 
face  of  the  prism  to  be  parallel  to  H and  \ inch  above  it,  The 
back  face  to  be  J inch  from  V. 

PLATE  X. 

The  ground  line  is  to  be  in  the  middle  of  the  sheet,  and  the 
location  arid  dimensions  of  the  figures  are  to  be  as  given.  The 
first  figure  shows  a rectangular  block  wdth  a rectangular  hole  cut 
through  from  front  to  back.  The  other  two  figures  represent  the 
same  block  in  different  positions.  The  second  figure  is  the  end  or 
profile  projection  of  the  block.  The  same  face  is  on  H in  all 
three  positions.  Be  careful  not  to  omit  the  shade  lines.  The 
figures  given  on  the  plate  for  dimensions,  etc.,  are  to  be  used  but 
not  repeated  on  the  plate  by  the  student. 


159 


68 


MECHANICAL  DRAWING 


PLATE  XI. 

Three  ground  lines  are  to  be  used  on  this  plate,  two  at  the  left 
4 \ inches  long  and  3 inches  from  top  and  bottom  margin  lines ; and 
one  at  the  right,  half  way  between  the  top  and  bottom  margins,  9| 
inches  long. 

The  figures  1,  2,  3 and  4 are  examples  for  finding  the  true 
lengths  of  the  lines.  Begin  No.  1 finch  from  the  border,  the 
vertical  projection  If  inches  long,  one  end  on  the  ground  line  and 
inclined  at  30°.  The  horizontal  projection  has  one  end  \ inch 
from  V,  and  the  other  inches  from  V.  Find  the  true  length  of 
the  line  by  completing  the  construction  commenced  by  swinging 
the  arc,  as  shown  in  the  figure. 

Locate  the  left-hand  end  of  No.  2 3 inches  from  the  border, 
1 inch  above  H,  and  § inch  from  V.  Extend  the  vertical  projection 
to  the  ground  line  at  an  angle  of  45°,  and  make  the  horizontal  pro- 
jection at  30°.  Complete  the  construction  for  true  length  as 
commenced  in  the  figure. 

In  Figs.  3 and  4,  the  true  lengths  are  to  be  found  by  complet- 
ing the  revolutions  indicated.  The  left-hand  end  of  Fig.  3 is  f 
inch  from  the  margin,  1\  inches  from  V,  and  If  inches  above  H. 
The  horizontal  projection  makes  an  angle  of  60°  and  extends  to  the 
ground  line,  and  the  vertical  projection  is  inclined  at  45°. 

The  fourth  figure  is  3 inches  from  the  border,  and  represents 
a line  in  a profile  plane  connecting  points  a and  b.  a is  If  inches 
above  H and  f inch  from  V ; and  b is  \ inch  above  H and 
inches  from  V. 

The  figures  for  the  middle  ground  line  represent  a pentagonal 
pyramid  in  three  positions.  The  first  position  is  the  pyramid  with 
the  axis  vertical,  and  the  base  § inch  above  the  horizontal.  The 
height  of  the  pyramid  is  2\  inches,  and  the  diameter  of  the  circle 
circumscribed  about  the  base  is  2\  inches.  The  center  of  the  circle 
is  6 inches  from  the  left  margin  and  If  inches  from  V.  Spaces 
between  figures  to  be  f inch. 

In  the  second  figure  the  pyramid  has  been  revolved  about  the 
right-hand  corner  of  the  base  as  an  axis,  through  an  angle  of  15°. 
The  axis  of  the  pyramid,  shown  dotted,  is  therefore  at  75°.  The 
method  of  obtaining  75°  and  15°  with  the  triangles  was  shown  in 


160 


II A 3-1  y-73 


EEBRUAR  Y 27y  /90/.  HERBERT  CHANDLER  CH/CAGO,  /LL 


MECHANICAL  DRAWING 


G9 


Part  I.  From  the  way  in  which  the  pyramid  has  been  revolved, 
all  angles  with  V must  remain  the  same  as  in  the  first  position ; 
hence  the  vertical  projection  will  be  the  same  shape  and  size  as 
before.  All  points  of  the  pyramid  remain  the  same  distance 
from  V.  The  points  on  the  plan  are  found  on  T-square  lines 
through  the  corners  of  the  first  plan  and  directly  beneath  the 
points  in  elevation.  In  the  third  position  the  pyramid  has  been 
swung  around,  about  a vertical  line  through  the  apex  as  axis, 
through  30°.  The  angle  with  the  horizontal  plane  remains  the 
same;  consequently  the  plan  is  the  same  size  and  shape  as  in  the 


A 


second  position,  but  at  a different  angle  with  the  ground  line. 
Heights  of  all  points  of  the  pyramid  have  not  changed  this  time, 
and  hence  are  projected  across  from  the  second  elevation.  Shade 
lines  are  to  be  put  on  between  the  light  and  dark  surfaces  as 
determined  by  the  45°  triangle. 

PLATE  XII. 

Developments. 

On  this  plate  draw  the  developments  of  a truncated  octagonal 
prism,  and  of  a truncated  pyramid  having  a square  base.  The 
arrangement  on  the  plate  is  left  to  the  student;  but  we  should 
suggest  that  the  truncated  prism  and  its  development  be  placed  at 


163 


TO 


MECHANICAL  DRAWING 


the  left,  and  that  the  development  of  the  truncated  pyramid  be 
placed  under  the  development  of  the  prism ; the  truncated  pyramid 
may  be  placed  at  the  right. 

The  prism  and  its  development  are  shown  in  Fig.  96.  The 
prism  is  3 inches  high,  and  the  base  is  inscribed  in  a circle  2J 
inches  in  diameter.  The  plane  forming  the  truncated  prism  is 
passed  as  indicated,  the  distance  A B being  1 inch.  Ink  a suffi- 
cient number  of  construction  lines  to  show  clearly  the  method  of 
finding  the  development. 

The  pyramid  and  its  development  are  shown  in  Fig.  97.  Each 
side  of  the  square  base  is  2 inches,  and  the  altitude  is  3J  inches. 


A 


Fig.  97. 


The  plane  forming  the  truncated  pyramid  is  passed  in  such  a 
position  that  A B equals  If  inches,  and  A C equals  2\  inches.  In 
this  figure  the  development  may  be  drawn  in  any  convenient 
position,  but  in  the  case  of  the  prism  it  is  better  to  draw  the 
development  as  shown.  Indicate  clearly  the  construction  by 
inking  the  construction  lines. 

PLATE  XIII. 

Isometric  and  ObSique  Projection. 

Draw  the  oblique  projection  of  a portable  closet.  The  angle  to 
be  used  is  45°.  Make  the  height  3|  inches,  the  depth  1^  inches, 
and  the  width  3 inches.  See  Fig.  98.  The  width  of  the  closet 


164 


MARCH  V,  /90/  HERBERT  CHANDLER  CH/CAGO,  /LL. 


MECHANICAL  DRAWING 


71 


is  to  be  shown  as  the  left-hand  face.  The  front  left-hand  lower 
comer  is  to  be  1 inch  from  the  left-hand  border  line  and  2 inches 
from  the  lower  border  line.  The  door  to  be  placed  in  the  closet 
should  be  1§  inches  wide  and  2|  inches  high.  Place  the  door 


centrally  in  the  front  of  the  closet,  the  bottom  edge  at  the  height 
of  the  floor  of  the  closet,  the  hinges  of  the  door  to  be  placed  on  the 
left-hand  side.  In  the  oblique  drawing,  show  the  door  opened 
at  an  angle  of  90  degrees.  The  thickness  of  the  material  of  the 
closet,  door,  and  floor  is  J inch. 

The  door  should  be  hung  so  that 
when  closed  it  will  be  flush  with 
the  front  of  the  closet. 

Make  the  isometric  drawing 
of  the  flight  of  steps  andend walls 
as  shown  by  the  end  view  in  Fig. 

99.  The  lower  right-hand  corner 
is  to  be  located  2\  inches  from 
the  lower,  and  5 inches  from  the 
right-hand,  margin.  The  base  of  the  end  wall  is  3J-  inches  long, 
and  the  height  is  2\  inches.  Beginning  from  the  back  of  the 
wall,  the  top  is  horizontal  for  § inch,  the  remainder  of  the  outline 
being  composed  of  arcs  of  circles  whose  radii  and  centers  are  given 


167 


72 


MECHANICAL  DRAWING 


in  the  figure.  The  thickness  of  the  end  wall  is  § inch,  and  both 
ends  are  alike.  There  are  to  be  five  steps;  each  rise  is  to  be 
f inch,  and  each  tread  | inch,  except  that  of  the  top  step,  which 
is  | inch.  The  first  step  is  located  § inch  back  from  the  corner 
of  the  wall.  The  end  view  of  the  wall  should  be  constructed  on  a 
separate  sheet  of  paper,  from  the  dimensions  given,  the  points  on 
the  curve  being  located  by  horizontal  co-ordinates  from  the  vertical 
edge  of  the  wall,  and  then  these  co-ordinates  transferred  to  the 
isometric  drawing.  After  the  isometric  of  one  curved  edge  has 
been  made,  the  others  can  be  readily  found  from  this.  The  width 
of  the  steps  inside  the  walls  is  3 inches. 

PLATE  XIV. 

Free=hand  Lettering. 

On  account  of  the  importance  of  free-hand  lettering,  the 
student  should  practice  it  at  every  opportunity.  For  additional 
practice,  and  to  show  the  improvement  made  since  completing 
Part  I,  lay  out  Plate  XIV  in  the  same  manner  as  Plate  I,  and  letter 
all  four  rectangles.  Use  the  same  letters  and  words  as  in  the  lower 
light-hand  rectangle  of  Plate  I. 

PLATE  XV. 

Lettering. 

First  lay  out  Plate  XV  in  the  same  manner  as  previous 
plates.  After  drawing  the  vertical  center  line,  draw  light  pencil 
lines  as  guide  lines  for  the  letters.  The  height  of  each  line  of 
letters  is  shown  on  the  reproduced  plate.  The  distance  be- 
tween the  letters  should  be  J inch  in  every  case.  The  spacing 
of  the  letters  is  left  to  the  student.  He  may  facilitate  his  work 
by  lettering  the  words  on  a separate  piece  of  paper,  and  finding 
the  center  by  measurement  or  by  doubling  the  paper  into  two 
equal  parts.  The  styles  of  letters  shown  on  the  reproduced  plate 
should  be  used. 


168 


F'LyATE 


! 

IN 


Ld 

CO 

GC 

O 


i 

i 


DETAIL  FROM  TEMPLE  OF  MARS  VENGEUR. 

An  example  of  classic  lettering,  conventional  shadows  and  rendering, 

Reproduced  by  permission  of  Massachusetts  Institute  of  Technology. 


SHADES  AND  SHADOWS, 


1.  The  drawings  of  which  an  architect  makes  use  can  be 
divided  into  two  general  kinds:  those  for  designing  the  building 
and  illustrating  to  the  client  its  scheme  and  appearance;  and 
“working  drawings”  which,  as  their  name  implies,  are  the  draw- 
ings from  which  the  building  is  erected.  The  first  class  includes 
“ studies,”  “ preliminary  sketches,”  and  “ rendered  drawings.” 
Working  drawings  consist  of  dimensioned  drawings  at  various 
scales,  and  full-sized  details. 

2.  It  is  in  the  drawings  of  the  first  kind  that  “shades  and 
shadows”  are  employed,  their  use  being  an  aid  to  a more  truthful 
and  realistic  representation  of  the  building  or  object  illustrated. 
All  architectural  drawings  are  conventional;  that  is  to  say,  they  are 
made  according  to  certain  rules,  but  are  not  pictures  in  the  sense 
that  a painter  represents  a building.  The  source  of  light  casting 
the  shadows  in  an  architectural  representation  of  a building  is  sup- 
posed to  be,  as  in  the  “picture”  of  a building,  the  sun,  but  the 
direction  of  its  rays  is  fixed  and  the  laws  of  light  observed  in  nature 
are  also  somewhat  modified.  The  purpose  of  the  architect’s  draw- 
ing is  to  explain  the  building,  therefore  the  laws  of  light  in  nature 
are  followed  only  to  the  extent  in  wdiich  they  help  this  explanation, 
and  are,  therefore,  not  necessarily  to  be  followed  consistently  or 
completely.  The  fixed  direction  of  the  sun’s  rays  is  a further  aid 
to  the  purpose  of  an  architectural  drawing  in  that  it  gives  all  the 
drawings  a certain  uniformity. 

3.  Definitions.  A clear  understanding  of  the  following  terms 
is  necessary  to  insure  an  understanding  of  the  explanations  which 
follow. 

4.  Shade:  When  a body  is  subjected  to  rays  of  light,  that 

portion  which  is  turned  away  from  the  source  of  light  and  which, 
therefore,  does  not  receive  any  of  the  rays,  is  said  to  be  in  shade. 
See  Fig.  1. 

5.  Shadow:  When  a surface  is  in  light  and  an  object  is 


173 


4 


SHADES  AND  SHADOWS 


placed  between  it  and  the  source  of  light,  intercepting  thereby 
some  of  the  rays,  that  portion  of  the  surface  from  which  light  is 
thus  excluded  is  said  to  be  in  shadow. 

6.  In  actual  practice  distinction  is  seldom  made  between 
these  terms  “shade”  and  “ shadow,”  and  “shadow”  is  generally 
used  for  that  part  of  an  object  from  which  light  is  excluded. 

7.  TJmbra:  That  portion  of  space  from  wThich  light  is 

excluded  is  called  the  umbra  or  invisible  shadow. 

(a)  The  umbra  of  a point  in  space  is  evidently  a line. 

(b)  The  umbra  of  a line  is  in  general  a plane. 

(c)  The  umbra  of  a plane  is  in  general  a solid. 

(d)  It  is  also  evident,  from  Fig.  1,  that  the  shadow  of  an  object  upon 
another  object  is  the  intersection  of  the  umbra  of  the  first  object  with  the 
surface  of  the  second  object.  For  example,  in  Fig.  1,  the  shadow  of  the  given 
sphere  on  the  surface  in  light  is  the  intersection  of  its  umbra  (in  this  case  a 
cylinder)  with  the  given  surface  producing  an  ellipse  as  the  shadow  of  the 
sphere. 

8.  Ray  of  light:  The  sun  is  the  supposed  source  of  light 

in  “ shades  and  shadows,” 
and  the  rays  are  propo- 
gated  from  it  in  straight 
lines  and  in  all  directions. 
Therefore,  the  ray  of  light 
can  be  represented  graph- 
ically by  a straight  line. 
Since  the  sun  is  at  an  in- 
finite distance,  it  can  be 
safely  assumed  that  the 
rays  of  light  are  all  par- 
allel. 

9.  Plane  of  light : A 
plane  of  light  is  any  plane  containing  a ray  of  light,  that  is,  in  the 
sense  of  the  ray  lying  in  the  plane. 

10.  Shade  line:  The  line  of  separation  between  the  portion 

of  an  object  in  light  and  the  portion  in  shade  is  called  the  shade  line. 

11.  It  is  evident,  from  Fig.  1,  that  this  shade  line  is  tlie 
boundary  of  the  shade.  It  is  made  up  of  the  points  of  tangency 
of  rays  of  light  tangent  to  the  object. 

12.  It  is  also  evident  that  the  shadow  of  the  object  is  the 
space  enclosed  by  the  shadow  of  the  shade  line.  In  Fig.  1,  the 


174 


SHADES  AND  SHADOWS 


shade  line  of  the  given  sphere  is  a great  circle  of  the  sphere.  The 
shadow  of  this  great  circle  on  the  given  plane  is  an  ellipse.  The 
portion  within  the  ellipse  is  the  shadow  of  the  sphere. 

NOTATION. 

13.  In  the  following  explanations  the  notation  usual  in 
orthographic  projections  will  be  followed: 

H = horizontal  co-ordinate  plane. 

Y ==  vertical  co-ordinate  olane. 

a = point  in  space. 

ay  = vertical  projection  (or  elevation)  of  the  point. 

ah  = horizontal  projection  (or  plan)  of  the  point. 

aws  = shadow  on  V of  the  point  a . 

«hs  = shadow  on  II  of  the  point  a. 

R = ray  of  light  in  space. 

Rv  = vertical  projection  (or  elevation)  of  ray  of  light. 

Rh  — horizontal  projection  (or  plan)  of  ray  of  light. 

GL=  ground  line,  refers  to  a plane  on  which  a shadow  is  to 
be  cast,  and  is  that  projection  of  the  plane  which  is  a line. 

14.  In  orthographic  projection  a given  point  is  determined  by  “project- 
ing” it  upon  a vertical  and  upon  a horizontal  plane.  In  representing  these 
planes  upon  a sheet  of  drawing  paper  it  is  evident,  since  they  are  at  right 
angles  to  each  other,  that  when  the  plane  of  the  paper 
represents  V( the  vertical  “co-ordinate”  plane),  the  hor- 
izontal “co-ordinate”  plane  H,  would  be  seen  and  rep- 
resented as  a horizontal  line,  Fig.  2.  Vice  versa , when 
the  plane  of  the  paper  represents  H(the  horizontal  co- 
ordinate plane) , the  vertical  co-ordinate  plane  V,  would 
be  seen  and  represented  by  a horizontal  line,  Fig.  2. 

15.  In  architectural  drawings  having  the  eleva- 
tion and  plans  upon  the  same  sheet,  it  is  customary  to 
place  the  “elevation,”  or  vertical  projection,  above  the 
plan,  as  in  Fig.  2. 

It  is  evident  that  the  distance  between  the  two 
ground  lines  can  be  that  which  best  suits  convenience. 

16.  As  the  problems  of  finding  the  shades  and 
shadows  of  objects  are  problems  dealing  with"  points, 
lines,  surfaces,  and  solids,  they  are  dealt  with  as  problems  in  Descriptive 
Geometry.  It  is  assumed  that  the  student  is  familiar  with  the’  principles  of 
orthographic  projection.  In  the  following  problems,  the  objects  are  referred 
to  the  usual  co-ordinate  planes,  but  as  it  is  unusual  in  architectural  drawings 
to  have  the  plan  and  elevation  on  the  same  sheet,  two  ground  lines  are  used 
instead  of  one. 

17.  Ray  of  Light.  The  assumed  direction  of  the  conven- 
tional ray  of  light  R,  is  that  of  the  diagonal  of  a cube,  sloping 
downward,  forward  and  to  the  right;  the  cube  being  placed  so 


FIG*  2 

Vertical 

Co-ordinate 

plane 

blang 


L-V  plane 

Horizontal 

Co-orainate 

plane 


6 


SHADES  AND  SHADOWS 


that  its  faces  are  either  parallel  or  perpendicular  to  H and  Y. 
Fig.  3 shows  the  elevation  and  plan  of  such  a cube  and  its  diagonal. 
It  will  be  seen  from  this  that  the  II  and  V projections  of  the 
ray  of  light  make  angles  of  45°  with  the  ground  lines . The  true 
angle  which  the  actual  ray  in  space  makes  with  the  co-ordinate 
planes  is  35°  15’  52'  This  true  angle  can  be  determined  as  shown 
in  Fig.  4.  Revolve  the  ray  parallel  to  either  of  the  co-ordinate 
planes.  In  Fig.  4,  it  has  been  revolved  parallel  to  Y,  hence  T is 
its  true  angle. 


FIG‘3 


18.  It  is  important  in  the  following  explanations  to  realize  the 
difference  in  the  terms  “ray  of  light,”  and  “projections  of  the  ray 
of  light.” 

SHADOWS  OF  POINTS. 

19.  Problem  I.  To  find  the  shadow  of  a given  point  on  a 
given  plane. 

Fig.  5 shows  the  plan  and  elevation  of  a given  point  a . 
It  is  required  to  find  its  shadow  on  a given  plane,  in  this  case  the 
Y plane.  The  shadow  of  the  point  a on  Y will  be  the  point  at 
which  the  ray  of  light  passing  through  a intersects  Y. 

Through  the  II  projection  of  the  given  point,  draw  Rh 
until  it  intersects  the  lower  ground  line.  This  means  that  the 
ray  of  light  through  a has  pierced  Y at  some  point.  The  exact 
point  will  be  on  the  perpendicular  to  the  ground  line,  where  Rv 
drawn  through  av  intersects  the  perpendicular.  The  point  aYS  is, 
therefore,  the  shadow  of  a on  the  Y plane. 

Rv  is  also  the  Y projection  of  the  umbra  of  the  point  a and 
it  will  be  seen  that  the  shadow  of  a on  Y is  the  intersection  of  its 
umbra  with  Y. 


176 


SHADES  AND  SHADOWS 


7 


20.  Fig.  6 shows  the  construction  for  finding  the  shadow  of 
a point  a on  H. 

21.  Fig.  7 shows  the  construction  for  finding  the  shadow  of 
a point  a , which  is  at  an  equal  distance  from  both  Y and  II.  Its 
shadow,  therefore,  falls  on  the  line  of  intersection  of  Y and  II. 

22.  Fig.  8 shows  the  construction  for  finding  the  imaginary 


shadow  of  the  point  a , situated  as  in  Fig.  5,  that  is,  nearer  the  Y 
plane  than  the  H.  The  actual  shadow  would  in  this  case  fall  on 
Y,  but  it  is  sometimes  necessary  to  find  its  imaginary  shadow  on  H. 
The  method  of  determining  this  is  similar  to  that  explained  in 
connection  with  Fig.  5. 

Draw  Rv  until  it  meets  the  ground  line  of  H. 

Erect  a perpendicular  at  this  point  of  intersection. 

Draw  Rh. 

The  intersection  ahs,  of  the  latter  and  the  perpendicular,  is  the 
required  imaginary  shadow  on  H of  the  point  a . 


23.  The  actual  shadow  of  a given  point,  with  reference  to 
the  two  co-ordinate  planes,  will  fall  on  the  nearer  co-ordinate  plane. 

24.  Fig.  9 shows  the  construction  for  finding  the  shadow  of 


8 


SHADES  AND  SHADOWS 


a given  point  a on  tlie  Y plane 
projections  of  the  point  are  given. 

25.  In  general,  the  finding  o 
on  a given  plane  is  the  same  as  th< 
section  of  its  umbra  with  that  pla\ 


when  the  vertical  and  profile 

f the  shadow  of  a given  point 
i finding  of  the  point  of  inter - 
xe.  To  obtain  this,  one  projec- 
tion of  the  given  plane  must 
be  a line  and  that  is  used  as 
the  ground  line . It  is  neces- 
sary to  have  a ground  line  to 
which  is  drawn  the  projection  of 
the  ray  of  light,  in  order  that  we 
as  pierced  the  given  plane. 


SHADOWS  OF  LINES. 


26.  Problem  II.  To  find  the  shadow  of  a given  line  on  a 
given  plane. 

A straight  line  is  made  up  of  a series  of  points.  Rays  of  light  passing 
through  all  of  these  points  would  form  a plane  of  light.  The  intersection  of 
this  plane  of  light  with  either  of  the  co-ordinate  planes  would  be  the  shadow 
of  the  given  line  on  that  plane.  This  shadow  would  be  a straight  line  because 
two  planes  always  intersect  in  a straight  line.  This  fact,  and  the  fact  that  a 
straight  line  is  determined  by  two  points,  enables  us  to  cast  the  shadow  of  a 
given  line  by  simply  casting  the  shadows  of  any  two  points  in  the  line  and 
drawing  a straight  line  between  these  points  of  shadow. 


In  Fig.  10,  avb v and  ahbh  are  the  elevation  and  plan 
respectively  of  a given  line  ab  in  space.  Casting  the  shadow  of 
the  ends  of  the  line  a and  b by  the  method  illustrated  in  Problem  1 
and  drawing  the  line  awsbvs,  we  obtain  the  shadow  of  the  given 
line  ab  on  Y. 

27.  Fig.  11  shows  the  construction  for  finding  the  shadow 
of  the  line  ab  when  the  shadow  falls  upon  II. 


178 


SHADES  AND  SHADOWS 


9 


28.  Fig.  12  shows  the  construction  for  finding  the  shadow 
of  a line  so  situated  that  part  of  the  shadow  falls  upon  V and  the 
remainder  on  H.  To  obtain  the  shadow  in  such  a case,  it  must  be 
found  wholly  on  either  one  of  the  co-ordinate  planes.  In  Fig.  12, 
it  has  been  found  wholly  on  Y,  ays  being  the  actual  shadow  of  that 
end  of  the  line,  and  Jvs  being  the  imaginary  shadow  of  the  end  b 
on  Y.  Of  the  line  avsbvs  we  use  only  the  part  &vscvs,  that 
being  the  shadow  wdiich  actually  falls  upon  Y. 


The  point  where  the  shadow  leaves  Y and  the  point  where  it 
begins  on  H are  identical,  so  that  the  beginning  of  the  shadow  on  H 
will  be  on  the  lower  ground  line  directly  below  the  point  cvs;  chs 
will  then  be  one  point  in  the  shadow  of  the  line  on  H,  and  casting 
the  shadow  of  the  end  b we  obtain  £hs.  The  line  <?hs5hs,  drawn 
between  these  points,  is  evidently  the  required  shadow  on  H. 

29.  Another  method  of  casting  the  shad- 
ow  of  such  a line  as  ab  is  to  determine  the 
entire  shadow  on  each  plane  independently. 

This  will  cause  the  two  shadows  to  cross  the 
ground  lines  at  the  same  point  c , and  of  these 
two  lines  of  shadows  we  take  only  the  actual 
shadows  as  the  required  result.  This  method 
involves  unnecessary  construction,  but  should 
be  understood. 

80.  Fig.  13  shows  the  construction  of  the 
shadow  of  a given  line  on  a plane  to  which 
it  is  parallel.  It  should  be  noted  that  the 
shadow  in  this  case  is  parallel  and  equal  in  length  to  the  given  hne. 

31.  Fig.  14  showrs  the  construction  of  the  shadow  of  a given 
line  on  a plane  to  wdiich  the  given  line  is  perpendicular.  It  is  to 


179 


10 


SHADES  AND  SHADOWS 


be  noted  that  the  shadow  coincides  in  direction  with  the  projection 
of  the  ray  of  light  on  that  plane , and  is  equal  in  length  to  the 
diagonal  of  a square  of  which  the  given  line  is  one  side. 

32.  Fig.  15  shows  the  construction  for  finding  the  shadow 
of  a curved  line  on  a given  plane.  Under  these  conditions  we  find, 
by  Problem  1,  the  shadows  of  a number  of  points  in  the  line — 
the  greater  the  number  of  points  taken  the  more  accurate  the  re- 
sulting shadow.  The  curve  drawn  through  these  points  of  shadow 
is  the  required  shadow. 

33.  In  Fig.  16  the  given  line  ab  is  in  space  and  the  prob- 
lem is  to  find  its  shadow  on  two  rectangular  planes  mnop  and  nrso , 
both  perpendicular  to  H. 

Consider  first  the  shadow  of  ab  on  the  plane  mnop.  The 
edge  no  is  the  limit  of  this  plane  on  the  right.  Therefore  from 
the  point  nh  draw  back  to  the 
given  line  the  projection  of  a 
ray  of  light.  This  45°  line  in- 
tersects the  given  line  at  ch.  It 
is  evident  that  of  the  given  line 


FI  GT6 


mv 

nv 

rv 

V' 

i 

/ ! 

' r 

IY  1 

i > 
i 

i 

i 

i 

► 

i 

i 

i 

p' i 

ov 

sv 

j 

i 

n${pb ! ! 

1 

1 

1 

1 

i 

i 

! 

! b 

— i / 

ab , the  part  ac  falls  on  the  plane  mnop  and  the  remainder,  cb , on 
the  plane  nrso. 

To  find  the  shadow  of  ac  on  the  left-hand  plane  we  must  first 
determine  our  ground  line.  The  ground  line  will  be  that  pro- 
jection of  the  plane  receiving  the  shadow  which  is  a line.  In  this 
example  the  vertical  projection  of  the  plane  mnop  is  the  rectangle 
mynyoypy.  This  projection  cannot,  therefore,  be  used  as  a GU 
The  plan,  or  H projection,  of  this  plane  is,  however,  a line  mhnh. 
This  line,  therefore,  will  be  used  as  the  ground  line  for  finding  the 
shadow  of  ac  on  mnop. 


180 


SHADES  AND  SHADOWS 


11 


We  find  the  shadow  of  a to  be  at  as  and  the  shadow  of  c at  0s, 
Problem  I.  The  line  ascs  is,  therefore,  a part  of  the  required 
shadow.  The  remaining  part,  csbs  is  found  in  a similar  manner. 

34.  The  above  illustrates  the  method  of  determining  the 

O 

GL  when  the  shadow  falls  upon  some  plane  other  than  a 
co-ordinate  plane.  In  case  neither  projection  of  the  given  plane 
is  a line,  the  shadow  must  be  deter- 
mined by  methods  which  will  be  ex- 
! • , X \ FIG-17 

plained  later.  !>  \ ' 

SHADOWS  OF  PLANES. 

35.  Problem  III.  To  find  the  shad= 
ow  of  a given  plane  on  a given  plane. 

Plane  surfaces  are  bounded  by 
straight  or  curved  lines.  Find  the 
shadows  of  the  bounding  lines  by  the 
method  shown  in  Problem  II.  The 
resulting  figure  will  be  the  required 
shadow. 

3G.  In  Fig.  IT,  the  plane  ale  is  so 
situated  that  its  shadow  falls  wholly 
upon  Y.  The  shadows  of  its  bounding  lines,  ah , be,  ca  have  been 
found  by  Problem  II. 

That  portion  of  the 
shadow  hidden  by  the 
plane  in  elevation  is 
cross-hatched  along  the 
edge  of  the  shadow  only. 
This  method  of  indicat- 
ing actual  shadows 
© 

which  are  hidden  by 
the  object  is  to  be  fol- 
lowed in  working  out 

the  problems  of  the  examination  plates. 

37.  Fig.  18  shows  the  construction  of  the  shadow7  of  a plane  on 
the  co-ordinate  plane  to  which  the  given  plane  is  parallel.  (In 
this  case  the  vertical  plane.)  It  is  to  be  observed  that  the  shadow 
is  equal  in  size  and  shape  to  the  given  plane. 

Fig.  19  shows  that,  in  case  of  a circle  parallel  to  one  of  the 


FIG-18 


181 


12 


SHADES  AND  SHADOWS 


co-ordinate  planes,  it  is  only  necessary  to  find  the  shadow  of  the 
center  of  the  circle  and  wTith  that  point  as  a center  construct  a 
circle  of  the  same  radius  as  that  of  the  given  circle. 

NOTE: 

39.  Any  point,  line,  or  plane  lying  in  a surface  is  considered  to  be  its 
own  shadow  on  that  surface. 

40.  A surface  parallel  to  a ray  of  light  is  considered  to  he  in  shade. 

41.  In  the  above  problems  the  points,  lines  and  planes  have  been  given 
in  vertical  and  horizontal  projection.  The  methods  for  finding  their  shadows 
are,  in  general,  equally  true  when  the  points,  lines  and  planes  are  given  by 
vertical  and  profile  projection  or  horizontal  and  profile  projection. 

SHADOWS  OF  SOLIDS. 

42.  The  methods  for  finding  the  shadows  of  solids  vary  with  the 
nature  of  the  given  solid.  The  shadows  of  solids  which  are  bounded 

o 

by  plane  surfaces,  none  of  which  are  parallel,  or  perpendicular,  to 
the  co-ordinate  planes,  can  in  general,  be  found  only  by  finding  the 
shadows  of  all  the  bounding  planes.  These  will  form  an  enclosed 
polygon,  the  sides  of  which  are  the  shadows  of  the  shade  lines  of 

the  object,  and  the  shade 
lines  of  the  solid  are  deter- 
mined in  this  way.  The 
following  is  an  illustration 
of  this  class  of  solids. 

43.  Problem  IV.  To 
find  the  shade  and  shadow 
of  a polyhedron,  none  of 
whose  faces  are  parallel  or 
perpendicular  to  theco=or= 
dinate  planes. 

Fig  20  shows  a poly- 
hedron in  such  a position 
and  of  such  a shape  that 
none  of  its  faces  are  per- 
pendicular or  parallel  to  the 
co-ordinate  planes.  It  is 
impossible,  therefore,  to  apply  to  this  figure  the  projections  of  the 
rays  of  light  and  determine  what  faces  are  in  light  and  wThat  in 
shade.  Consequently  we  cannot  determine  the  shade  line  whose 
shadows  would  form  the  shadow  of  the  object. 


18g 


SHADES  AND  SHADOWS 


13 


Under  these  circumstances  we  must  cast  the  shadows  of  all 
the  boundary  edges  of  the  object . Some  of  these  lines  of  shadow 
will  form  a polygon,  the  others  will  fall  inside  this  polygon.  The 
edges  of  the  object  whose  shadows  form  the  bounding  lines  of  the 
polygon  of  shadow  are  the  shade  lines  of  the  given  object.  Know- 
ing the  shade  lines,  the  light  and  shaded  portions  of  the  object  can 
now  be  determined,  since  these  are  separated  by  the  shade  lines. 

In  a problem  of  this  kind  care  should  be  taken  to  letter  or 
number  the  edges  of  the  given  object . 

44.  The  edges  of  the  polyhedron  shown  in  Fig.  20  are  ab , 
be,  cd,  da,  ac  and  bd. 

Cast  the  shadows  of  each  of  these  straight  lines  by  the  method 
shown  in  Problem  II. 

We  thus  obtain  a polygon  bounded 
by  the  lines  bvscYS,  cYSaYS,  aysbws,  and 
this  polygon  is  the  shadowof  the  given 
solid. 

The  lines  which  cast  these  lines  of 
shadow,  bYScxs,  cYSaws,  and  aYSUs  are 
therefore  the  shade  lines  of  the  object, 
and,  therefore,  the  face  abc  is  in  light 
and  the  faces  abd,  bed  and  acd  are 
in  shade. 

The  shadows  of  the  edges  bd,  dc,  and 
ad  falling  within  the  polygon,  indi- 
cate that  they  are  not  shade  lines  of 
the  given  object,  and,  therefore,  they 
separate  two  faces  in  shade  or  two 
faces  in  light.  In  this  example  bd 
and  cd  separate  two  dark  faces. 

In  architectural  drawings  the  object  usually  has  a sufficient 
number  of  its  planes  perpendicular  or  parallel  to  the  co-ordinate 
planes,  to  permit  its  shadow  being  found  by  a simpler  and  more 
direct  method  than  the  one  just  explained. 

45.  Problem  V.  To  find  the  shade  and  shadow  of  a prism 
on  the  co-ordinate  planes,  the  faces  of  the  prism  being  perpen= 
dicular  or  parallel  to  the  V and  H planes. 

In  Fig.  21  such  a prism  is  shown  in  plan  and  elevation.  The 


FIG*  21 


183 


14 


SHADES  AND  SHADOWS 


elevation  shows  it  to  be  resting  on  H,  and  the  plan  shows  it  to  be 
situated  in  front  of  Y,  its  sides  making  angles  with  V.  Since 
its  top  and  bottom  faces  are  parallel  to  H and  its  side  faces  per- 
pendicular to  that  plane,  we  can  apply  the  projections  of  the  rays 
of  light  to  the  plan  and  determine  at  once  which  of  the  side  faces 
are  in  light  and  which  in  shade.  The  projections  of  the  rays  R1 
and  R2  show  that  the  faces  abgf  and  adif  receive  the  light  directly, 
and  that  the  two  other  side  faces  do  not  receive  the  rays  of  light 
and  are,  therefore,  in  shade.  The  edges  bg  and  di  are  two  of 
the  shade  lines.  R3  and  R4  are  the  projections  of  the  rays  which 
are  tangent  to  the  prism  along  these  shade  lines. 

Applying  the  projection  R5  in  the  elevation  makes  it  evident 
that  the  top  face  of  the  prism  is  in  light  and  the  bottom  face  is  in 
shade  since  the  prism  rests  on  H.  This  determines  the  light  and 
shade  of  all  the  faces  of  the  prism,  and  the  other  shade  lines  would 
therefore  be  be  and  ed. 

Casting  the  shadow  of  each  of  these  shade  lines,  we  obtain 
the  required  shadow  on  Y and  H. 

It  is  evident  that  the  shadows  of  the  edges  bg  and  di  on 
H will  be  45°  lines  since  these  edges  are  perpendicular  to  H (§  31) 
Also,  their  shadows  on  Y will  be  parallel  to  the  lines  themselves 
since  these  shade  lines  are  parallel  to  Y.  (§  30) 

46.  In  general,  to  find  the  shadow  of  an  object  whose  planes 
are  parallel  or  perpendicular  to  II  or  Y : 

(1)  Apply  to  the  object  the  projections  of  the  ray  of  light  to 
determine  the  lighted  and  shaded  faces. 

(2)  These  determine  the  shade  lines. 

(3)  Cast  the  shadows  of  these  shade  lines  by  the  method  fol- 
lowed in  Problem  II. 

47.  Problem  VI.  To  find  the  shade  and  shadow  of  one 
object  on  another. 

In  Fig.  22  is  shown  in  plan  and  elevation  a prism  B,  resting 
on  II  and  against  Y.  Upon  this  prism  rests  a plinth  A:  To  find 

the  shadow  of  the  plinth  on  the  prism  and  the  shadow  of  both  on 
the  co-ordinate  planes.  Since  these  objects  have  their  faces  either 
perpendicular  to,  or  parallel  to,  the  co-ordinate  planes,  we  can  deter- 
mine immediately  the  light  and  shade  faces  and  from  them  the 
shade  lines. 


184 


SHADES  AND  SHADOWS 


15 


48.  Considering  first  tlie  plinth  A,  it  is  evident  that  its  top, 
left-hand  and  front  faces  will  receive  the  light,  that  the  lower  and 
right-hand  faces  will  be  in  shade.  The  back  face  resting  against 
the  Y plane  will  be  its  own  shadow  on  Y.  (§  39)  The  shade  lines  of 
A will  be,  therefore,  cf^fg^  go  and  cd . 

Cast  the  shadows  of  these  lines.  A rests  against  Y and  part 
of  its  shadow  will  fall  on  Y ; also,  since  it  rests  on  B the  remainder 
will  fall  on  B.  Begin  with  the  point  <?,  one  end  of  the  shade  line; 
this  point,  lying  in  Y,  is  its  own  shadow  on  Y.  (&  39). 

The  line  ef  being  perpendicular  to  Y,  its  shadow,  or  as 
much  of  its  shadow  as  falls  on  Y,  will  be,  therefore,  a 45°  line 
drawn  from  ey.  The  point  th,  in  plan,  shows  the  amount  of  the 
line  ef  which  falls  on  Y,  the  rest  tf  falls  on  the  side  face  of  the 
prism,  and  this  shadow  is  not  visible  in  elevation  or  plan. 

The  shadow  of  the  point  f evidently  falls  on  the  edge  of  the 
prism  at  fs , see  plan.  This  point  f 
is  one  end  of  the  shade  lineal/,  there- 
fore f is  one  point  in  the  shadow  of 
fg  on  the  front  face  of  the  prism  B. 

The  \msfg  being  parallel  to  this  front 
face,  its  shadow  will  be  parallel  to  the 
line,  therefore  from  the  pointy  we 
draw  the  horizontal  line f*r*m 

If  from  the  point  r*  we  draw  the 
projection  of  a ray  of  light  back  to 
the  shade  lin efYgY  we  determine  the 
amount  of  the  line  casting  a shadow 
on  the  front  face  of  B,  that  is  to  say,  the 
distance/V7.  The  shadow  of  the  remainder,  rvgv,  falls  beyond  the 
prism  on  the  Y plane,  and  is  evidently  the  line  rvs</vs.  Thus 
the  shadow  of  the  shade  line  from  e to  g has  been. determined. 

The  next  portion  of  the  shade  line,  gc , is  a vertical  line  and 
we  have  already  obtained  the  shadow  of  the  end  g.  Since  it  is  a 
vertical  line  its  shadow  on  Y will  be  vertical  and  equal  in  length. 
Therefore  draw  gyscvs. 

There  remains  now  only  the  edge,  cd , of  which  to  cast  the 
shadow.  The  end  d being  in  the  Y plane  must  be  its  own  shadow 
on  that  plane.  (§  39)  We  have  already  found  the  shadow  of  the 


185 


16 


SHADES  AND  SHADOWS 


other  end  c,  at  cys.  Therefore  dycys  is  the  shadow  of  do  and 
completes  the  outline  of  the  shadow  of  the  plinth. 

It  will  be  noted  that  dycys  is  a 45°  line,  which  wTould  be 
expected  since  the  edge  do  is  perpendicular  to  V, 

49.  Considering  next  the  prism  B,  we  find  by  applying  the 
projections  of  the  rays  of  light  to  the  plan,  that  the  front  and 
left-hand  faces  are  in  light,  and  that  the  right-hand  face  is  in 
shade.  Therefore  the  only  shade  line  in  this  case  is  the  edge 
mn.  The  upper  part  of  this,  myr]s  is  in  the  shade  of  the 
plinth  and  therefore  cannot  cast  any  shadow. 


It  is  to  be  noted  that  the  ray  of  light  from  the  point  ry  in  the 
plinth  A passes  through  the  point  r*  in  the  shade  line  of  the 
prism  B.  In  finding  the  shadow  of  this  point  at  rys  wTe  therefore 
have  found  the  shadow  also  of  one  end  of  the  shade  line  nr. 
Since  nr  is  vertical,  its  shadow  will  be  vertical  on  V.  There- 
fore draw  ryswys.  This  line  completes  the  shadow  of  the  two  objects 
upon  the  V plane. 


186 


SHADES  AND  SHADOWS 


17 


From  the  point  of  shadow  w vs  draw  the  Y projection  of  the 
ray  back  to  the  line  nyr*.  This  shows  how  much  of  the  total 
line  nr  falls  upon  Y,  and  how  much  upon  II. 

The  shadow  on  II  of  the  portion  nw  will  be  a 45°  line  since 
nw  is  perpendicular  to  H.  The  point  n being  in  the  II  plane 
is  its  own  shadow  on  that  plane. 

It  is  to  be  noted  that  the  point  whs  is  on  the  perpendicular 
directly  below  wys. 

50.  Problem  VII.  To  find  the  shade  and  shadow  of  a pedestal. 

Fig.  23  shows  the  plan  and  elevation  of  a pedestal  resting  on 
the  ground  and  against  a vertical  wall.  This  is  an  application  of 
the  preceding  problem  in  finding  the  shades  and  shadows  of  one 
object  upon  another.  The  profile  of  the  cornice  moulding  on 
the  left,  at  A,  can  be  used  as  a profile  projection  in  finding  the 
shadows  of  those  mouldings  on  themselves  and  upon  the  front  face 
B,  of  the  pedestal.  By  drawing  the  profile  projections  of  the  rays 
tangent  to  this  profile  of  mouldings,  it  will  be  seen  what  edges  are 
shade  lines  and  where  their  shadows  will  fall  on  the  surface  of  B. 
The  line  ayby  can  be  assumed  to  be  the  profile  projection  of  the 
front  face  of  B,  and  being  a line  is  used  as  the  ground  line  for 
finding  the  shadow  on  B.  As  this  collection  of  mouldings  is 
parallel  to  the  Y plane  their  shades  and  shadows  will  be  parallel 
in  the  elevation.  Otherwise  the  shadows  of  this  pedestal  are  found 
in  a manner  similar  to  the  preceding  problem. 

51.  Problem  VIII.  To  find  the  shadow  of  a chimney  on  a 
sloping  roof. 

Fig.  23a  shows  in  elevation  and  side  elevation  the  chimney 
and  roof.  The  chimney  itself  being  made  up  of  prisms  with  their 
planes  parallel  or  perpendicular  to  the  Y plane,  its  light  and  shade 
faces  can  be  determined  at  once,  as  in  Problem  Y.  It  will  be 
evident  from  the  figure  that  the  top,  front,  and  left-hand  faces  of 
the  chimney  in  elevation  will  be  in  light.  The  remaining  faces 
will  be  in  shade,  and  the  shade  lines  will  be  therefore,  yd,  on  the 
back,  do,  cb,  and  bx.  Not  all  of  bx  and  yd  will  cast  shadows 
for  the  shadow  of  the  flat  band,  running  around  the  upper  part  of 
the  chimney,  will  cause  a portion  of  these  two  lines  yd  and  bx 
to  be  in  shadow  and  such  portions  cannot  cast  any  shadows.  (See 
Problem  YI — the  shadow  of  one  object  upon  another.) 


187 


J8 


SHADES  AND  SHADOWS 


It  is  evident  that,  to  find  the  shadow  of  the  shade  line  of  the 
chimney  upon  the  sloping  roof,  we  must  have  for  a ground  line 
a projection  of  the  roof  which  is  a line.  The  roof  in  elevation 
is  projected  as  a plane,  but  the  side  elevation  (or  in  other  words 
the  profile  projection)  shows  the  roof  projected  as  a line  in  the 
line  Ap^p.  This  line  will  be  then  the  ground  line  for  finding 
the  shadow  of  any  point  in  the  chimney  on  the  roof.  For  example, 
take  the  point  b.  If  we  draw  the  profile  projection  of  the  ray 
through  the  point  l/v  until  it  intersects  the  ground  line  Ap^p,  and 
draw  from  this  point  of  intersection  a horizontal  line  across  until 
it  intersects  the  vertical  projection  of  the  ray  drawn  through  by,  this 
last  point  of  intersection  bs , will  be  the  shadow  of  b upon  the  roof. 

In  a similar  manner  the  shadow  of  any  point  or  line  in  the 
chimney  can  be  found  on  the  roof. 


• . 

Before  completing  the  shadow  of  the  chimney  upon  the  roof 
let  us  consider  the  shadow  of  the  fiat  band  on  the  main  part  of  the 
chimney.  This  band  projects  the  same  amount  on  all  sides.  On 
the  left-hand  and  front  faces  it  will  cast  a shadow  on  the  chimney 
proper.  Only  the  shadow  on  the  front  face  will  be  visible  in 
elevation.  To  find  this,  draw  the  profile  projection  of  the  ray 
through  the  point  (p>  until  it  intersects  the  line  ap^p,  the  profile 
projection  of  the  front  face.  From  this  point  qf  draw  a horizontal 
line  across  until  it  meets  the  vertical  projection  of  the  ray  drawn 
through  qy.  From  ^v,  the  shadow  of  qvwy  on  the  front  face  will 
be  parallel  to  qywy,  for  that  line  is  parallel  to  that  face;  therefore 
draw  q?zf 


188 


An  example  of  conventional  shadows  and  rendering. 

Reproduced  by  permission  of  Massachusetts  Institute  of  Technology. 


SHADES  AND  SHADOWS 


19 


N ow  that  the  visible  shadows  on  the  chimney  itself  have  been 
determined,  its  shadow  on  the  roof  can  be  found  as  explained  in 
the  first  part  of  this  problem.  A portion  of  the  shade  line  of  the 
flat  band,  wYny,  etc.,  falls  beyond  the  chimney  on  the  roof, 

as  shown  by  the  line  zsws , wsn3,  etc. 

52.  It  is  to  be  noted  in  the  shadow  on  the  roof  that: 

(a)  The  shadows  of  the  vertical  edges  of  the  chimney  make 
angles  with  a horizontal  line  equal  to  the  angle  of  the  slope  of 
the  roof  { in  this  case  60°). 

i(b)  The  horizontal  edges  which  are  parallel  to  V cast 
shadows  which  are  parallel  to  these  same  edges  in  the  chimney. 

(c)  The  horizontal  edges  which  are  perpendicular  to  V cast 
shadows  which  make  angles  of  45°  with  a horizontal  line. 

53.  The  above  method  would  also  be  used  in  finding  shad- 
ows on  sloping  surfaces  when  the  objects  are  given  in  elevation  and 
side  elevation,  as,  for  example,  a dormer  window. 

54.  Problem  IX.  To  find  the  shades  and  shadows  of  a 
hand  rail  on  a flight  of  steps  and  on  the  ground. 

Fig.  24  shows  the  plan  and  elevation  of  a flight  of  four  steps 
situated  in  front  of  a vertical  wall,  with  a solid  hand  rail  on  either 
side,  the  hand  rails  being  terminated  by  rectangular  posts.  At  a 
smaller  scale  is  shown  a section  through  the  steps  and  the  slope  of 
the  hand  rail. 

This  problem  amounts  to  finding  the  shadow  of  a broken  line, 
that  is  to  say,  the  shade  line,  on  a series  of  planes.  Each  of  the 
planes  requires  its  own  ground  line,  which  in  the  case  of  each  plane 
will  be  that  projection  of  the  plane  wdiich  is  a line.  Since  the 
planes  of  the  steps  and  rails,  with  one  exception,  are  all  parallel 
or  perpendicular  to  the  co-ordinate  planes  we  can  determine  at 
once  what  planes  are  in  light  and  what  in  shadow  and  thus  deter- 
mine the  shade  line. 

55.  An  inspection  of  the  figure  will  make  it  evident  that  the 
“treads”  of  the  steps,  A,  B,  C,  D and  the  “ risers,”  M,  N,  O,  P are 
all  in  lio-ht.  Of  the  hand  rail  it  will  be  evident  also  that  the  left- 

o 

hand  face,  the  top,  and  the  front  face  of  the  post  are  in  light.  The 
remaining  faces  are  in  shade.  This  is  true  of  both  rails;  there- 
fore, in  one  case  we  must  find  the  shadow  of  a broken  line,  dbcdef 
on  the  vertical  wall  and  on  the  steps,  and  then  find  the  shadow  of 


191 


20 


SHADES  AND  SHADOWS 


the  broken  line  mnojpqr  on  the  vertical  wall  and  on  the  ground. 

56.  Beo-inninor  with  the  shadow  of  the  left-hand  rail,  the 
shadow  of  the  point  a on  the  wall  is  evidently  ceY , since  a lies  in 
the  plane  of  the  vertical  wall  (§  39) 

The  line  ab  is  perpendicular  to  Y hence  its  shadow  will  be  a 


45°  line,  the  point  bys  being  found  by  Problem  I.  The  shadow 
of  be , the  sloping  part  of  the  rail,  will  fall  partly  on  the  vertical 
wall  and  partly  on  the  treads  and  risers.  We  have  already  found 
the  shadow  of  the  end  b on  Y in  the  point  bys.  The  shadow  of  c 


192 


SHADES  AXD  SHADOWS 


21 


on  V,  found  by  Problem  I will  be  cys.  Tbe  portion  bvsyYS  is  the 
part  of  tbe  shadow  of  this  line  be  that  actually  falls  on  the  wall, 
the  steps  preventing  the  rest  of  the  line  from  falling  on  V. 

The  line  of  shadow  now  leaves  the  vertical  wall  at  the  point 
</as,  directly  below  yYS.  The  ground  line  for  finding  the  shadow 
on  this  upper  tread  will  evidently  be  the  line  Av,  since  that  line 
is  the  projection  of  this  tread  which  is  a line.  The  horizontal 
projection  of  the  tread  is  a plane  between  the  lines  and 

bhn\  We  have  now  determined  our  GL  and  we  also  have  one 
point,  </as  in  the  required  shadow  on  the  upper  tread  A.  It  re- 
mains to  find  the  shadow  of  the  end  c on  A.  Draw  the  projection 
of  the  ray  through  cY  until  it  meets  the  line  Av,  drop  a perpen- 
dicular until  it  intersects  the  projection  of  the  ray  drawn  through 
ch  at  the  point  cas.  The  point  <?as  lies  on  the  plane  A extended. 
Draw  the  line  y^c*5.  The  portion  yashas  is  the  part  actually 
falling  on  the  tread  A. 

From  thispjoint  //,  the  shadow  leaves  tread  A and  falls  on  the 
upper  riser  At.  The  shadow  will  now  show  in  elevation  and  begin 
at  the  point  hms  directly  above  the  point  Aas. 

We  now  determine  a n ew ground  line  and  it  will  be  t]urt  pro- 
jection of  the  upper  riser  J/,  which  is  a line.  The  vertical  pro- 
jection of  AI  is  a plane  surface  between  the  lines  Av  and  Bv.  The 
II  projection  of  the  riser  AI  is  the  line  AIh,  therefore  this  is  our 
GL,  and  we  find  the  shadow  on  AT  in  a manner  similar  to  the  find- 
ing of  the  shadow  on  A,  just  explained.  Bear,  in  mind  that  we 
have  one  point  Ams,  already  found  in  this  required  shadow  on  M. 

In  a like  manner  the  shadow  of  the  remainder  of  the  shade 
line  is  found  until  the  pointy*  is  reached,  which  is  its  own  shadow 
on  the  ground.  (39) 

57.  It  is  to  be  noted  that,  since  the  plane  of  the  vertical 
wall  and  the  planes  of  the  risers  are  all  parallel,  the  shadows  on 
these  surfaces  of  the  same  line  are  all  parallel.  For  a similar  reason, 
the  shadows  of  the  same  line  on  the  treads  and  ground  will  be  paral- 
lel. This  fact  serves  as  a check  as  to  the  correctness  of  the  shadow. 

Also  note  in  the  plan  that  the  shadow  of  the  vertical  edge  ef 
of  the  post  is  a continuous  45°  line  on  the  ground,  the  lower  tread 
D,  and  on  the  next  tread  C,  above.  While  this  line  of  shadow 
on  the  object  is  of  course  in  reality  a broken  line , it  appears  in 
horizontal  projection  on  plan  as  a continuous  line. 


193 


00 


SHADES  AND  SHADOWS 


The  shadow  of  the  shade  line  of  the  right-hand  rail  is  simply 
the  shadow  of  a broken  line  on  the  co-ordinate  planes,  and  requires 
no  detailed  explanation. 

58.  Problem  X.  To  find  the  shade  and  shadow  of  a cone. 

The  finding  of  the  shadow  of  a cone  is,  in  general,  similar  to 

o 7 O 7 

finding  the  shadow  of  the  polyhedron  none  of  whose  planes  are 
perpendicular  or  parallel  to  the  co-ordinate  planes. 

It  is  impossible  to  determine  at  the  beginning,  the  shade  ele- 
ments of  the  cone  whose  shadows  give  the  shadow  of  the  cone,  and 
we  first  find  the  shadow  of  the  cone  itself  and  from  that  determine 

its  shade  elements:  that  is  to  say 
we  reverse  the  usual  process  in 
determining  the  shadow  of  an 

o 

object. 

59.  Fig.  25  shows,  in  elevation 
and  plan,  a cone  whose  apex  is  a 
and  whose  base  is  bcde,  etc.  The 
axis  is  perpendicular  to  H and  the 
cone  is  so  situated  that  its  shadow 
falls  entirely  on  the  Y plane. 

60.  It  is  evident  that  the  shad- 
ow of  the  cone  must  contain  the 
shadow  of  its  base  and  also  the 
shadow  of  its  apex.  Therefore, 
if  we  find  the  shadow  of  its  apex 
by  Problem  I,  and  then  find  the 
shadow  of  its  base  by  Problem 
III  and  draw  straight  lines  from 

o 

the  shadow  of  the  apex  tangent  to  the  shadow  of  the  base,  the 
resulting  figure  will  be  the  required  shadow  of  the  cone. 

61.  This  has  been  done  in  Fig.  25,  in  which  «Vs  is  the 

o 

shadow  of  the  apex  a . The  ellipse  bYScYSdYS,  etc.,  is  the  shadow  of 
the  base,  found  by  assuming  a sufficient  number  of  points  in  the 
perimeter  of  the  base  and  finding  their  shadows.  The  ellipse 
drawn  through  these  points  of  shadow  is  evidently  the  shadow  of 
the  base.  From  the  point  aYS  the  straight  lines  aYSsYS  and  aYSxYS 
were  drawn  tangent  to  the  ellipse  of  the  shadow.  This  determined 
the  shadow  on  Y of  the  cone.  The  lines  aYSsYS  and  aYSxYS  are 


194 


SHADES  AND  SHADOWS 


23 


the  shadows  of  the  shade  elements  of  the  cone.  It  remains  to  de- 
termine these  in  the  cone  itself.  Any  point  in  the  perimeter  of 
the  shadow  of  the  base  must  have  a corresponding  point  in  the 
perimeter  of  the  base  of  the  cone,  and  this  can  be  determined  by 
drawing  from  the  point  in  the  shadow  the  projection  of  the  ray  back 
to  the  perimeter  of  the  base.  Therefore  if  we  draw  45°-lines  from 
the  point  xys  and  svs  back  to  the  line  cymy  in  the  elevation,  we 
determine  the  points  xy  and  sy.  The  lines  drawn  from  these  points 
to  the  apex  ay  are  the  shade  elements  of  the  cone.  They  can  be 
determined  in  plan  by  projection  from  the  elevation.  The  cross- 
hatched  portion  of  the  cone  indicates 
its  shade.  It  will  be  observed  that 
but  little  of  it  is  visible  in  elevation. 

62.  When  the  plane  of  the  base  of 
the  cone  is  parallel  to  the  plane  on 
which  the  shadow  falls,  as  in  Fio-.  26, 
the  work  of  finding  its  shade  and  shad- 
ow  is  materially  reduced,  for  the  shad- 
ow of  the  base  can  then  be  found  by 
findinor  the  shadow  of  the  center  b of 

o 

the  base  and  drawing  a circle  of  the 

o 

same  radius.  (See  Fig.  19) 

63.  In  general,  to  find  the  shadow 
of  any  cone,  find  the  shadow  of  its 
apex,  then  the  shadow  of  its  base,  draw 
straight  lines  from  the  former,  tang 
ent  to  the  latter.  Care  should  be 
taken,  however,  that  both  the  shadow  of  the  apex  and  the  shadow 
of  the  base  are  found  on  the  same  plane. 

64.  It  is  to  be  noted  that  in  a cone  whose  elements  make  an 
angle  of  35°-lo-52 " or  less , that  is,  making  the  true  angle  of  the 
ray  of  light  or  less,  with  the  co-ordinate  plane,  the  shadow  of  the 
apex  will  fall  within  the  shadow  of  the  base,  and,  therefore,  the 
cone  will  have  no  shade  on  its  conical  surface. 

65.  Problem  XI.  To  find  the  shade  and  shadow  of  a right 
cylinder. 

In  Fig.  27  is  shown  the  plan  and  elevation  of  a right  cylinder 
resting  on  H.  The  rays  of  light  will  evidently  strike  the  top  of 


195 


24 


SHADES  AND  SHADOWS 


the  cylinder  and  the  cylindrical  surface  shown  in  the  plan  between 
the  points  hh  and  dh.  At  these  points,  the  projections  of  the  ray 
of  light  are  tangent,  and  these  points  in  plan  determine  the  shade 
elements  of  the  cylinder  in  elevation.  These  shade  elements, 
ayhY  and  are  the  lines  of  tangency  of  planes  of  light  tangent 
to  the  cylinder.  The  shadow  of  these  lines  ctb  and  cd , together 
with  the  shadow  of  the  arc  aefg , etc.,  of  the  top  of  the  cylinder, 
form  the  complete  shadow  of  the  cylinder. 

Since  ah  and  cd  are  perpendicular  to  H,  as  much  of  their 
shadow  as  falls  upon  the  H plane  will  be  45°  lines  drawn  from 
and  cZh  respectively.  In  one  case  the  amount  is  the  line  nYbY,  in 
the  other  hYdY.  The  remainder  of  the  lines  will  fall  upon  Y and 
this  is  found  by  Problem  II.  These  shadows  on  Y will  evidently 

The  shadow  of  the  shade  line 
aef(j , etc.,  on  Y will  be  found 
by  Problem  II.  (§32) 

66.  If  the  cylinder  had  been 
placed  so  that  the  whole  of  its 
shadow  fell  upon  II,  the  shadow 
of  the  shade  line  of  the  top  would 
have  been  found  by  finding  the 

J o 

shadow  of  the  center  of  the  circle 
and  drawing  a circle  of  the  same 
radius,  since  the  plane  of  the  top 
is  parallel  to  H.  (§  38) 

67.  Problem  XII.  To  find 
the  shade  and  shadow  of  an 
oblique  cylinder. 

In  Fig.  28  is  shown  the  plan 
and  elevation  of  an  oblique  cylin- 
der whose  vertical  section  is  a circle. 

68.  Unlike  the  right  cylinder  we  cannot  apply  to  the  plan 
or  elevation  the  projections  of  the  ray  and  determine  at  once  the 
location  of  the  shade  elements.  To  find  the  shadow  of  an  oblique 
cylinder  we  proceed  in  a manner  similar  to  finding  the  shade  and 
shadow  of  a cone;  that  is,  we  find  first  the  shadow  of  the  cylinder 
and  from  that  shadow  determine  the  shade  elements. 


be  parallel  to  aYny  and  cYli 


av  <zv  fv  cvivhv 
m/wmnmriiwm — 

FT? 


FIG*2^ 


190 


SHADES  AND  SHADOWS 


6(J.  In  Fig.  28  the  top  and  base  of  the  oblique  cylinder  have 
been  assumed,  for  convenience,  parallel  to  one  of  the  co-ordinate 
planes.  The  shadow  of  the  cylinder  will  contain  the  shadows  of 
the  top  and  base,  hence  if  we  find  their  shadows  and  draw  straight 
lines  tangent  to  these  shadows,  we  shall  obtain  the  required  shadow 
of  the  cylinder. 

70.  In  Fig.  28,  the  top  and  bottom  being  circles,  the  shadows 
of  their  centers  a and  b are  found  at  avs  and  Z»vs,  and  circles  of  the 
same  radius  are  drawn.  Then  the  lines  mysnvs  and  ovs/?vs  are 


drawn  tangent  to  these  circles.  The  resulting  figure  is  the  required 
shadow  wholly  on  V.  Projections  of  the  ray  are  then  drawn  back 
from  mvs,  n™,  6>vs  and  pvs  respectively  to  the  perimeter  of  the  top 
and  base.  Their  points  of  intersection  mv,  ny , 6>v  and  are  the 
ends  of  the  shade  elements  in  the  elevation.  They  can  be  found 
in  plan  by  projection.  An  inspection  of  the  figure  will  make  it 
evident  what  portions  of  the  cylindrical  surface  between  these 
shade  elements  will  be  light  and  what  in  shade. 

71.  In  this  problem  it  will  be  seen  that  the  shadow  does  not 
fall  wholly  upon.  Y.  The  shadow  leaves  Y at  the  points  x vs  and  yvs 
and  will  evidently  begin  on  H at  points  directly  below,  as  .£hs 
and  yhs. 


197 


26 


SHADES  A HD  SHADOWS 


If  projections  of  the  ray  are  drawn  back  to  the  object  in  plan 
and  elevation  from  these  points,  a?vs,  yys,  xhs , and  yhs,  they  will 
determine  the  portion  of  the  shade  line  which  casts  its  shadow  on 
H.  It  is  evident  that  in  this  particular  object  it  is  that  portion 
of  the  shade  line  of  the  top  between  the  points  p and  y and  the 
portion  xp,  of  one  of  the  shade  elements.  The  shadows  of  these 
lines  are  found  on  H by  Problem  II. 


USE  OF  AUXILIARY  PLANES. 


72.  In  finding  shadows  on  some  of  the  double-curved  sur- 
faces of  revolution,  such  as  the  surface  of  the  spherical  hollow, 
the  scotia  and  the  torus,  we  can  make  use  of  auxiliary  planes  to 

advantage,  when  the  plane  of 
the  line  whose  shadow  is  to  he 
cast  is  parallel  to  one  of  the 
co-ordinate  planes . 

73.  Problem  XIII.  To  find 
the  shadow  in  a spherical  hol= 
low. 

Fig.  29  shows  in  plan  and 
elevation  a spherical  hollow 
whose  plane  has  been  assumed 
parallel  to  Y. 

Applying  to  the  elevation, 
the  projections  of  the  ray  II, 
we  determine  the  amount  of  the 
edge  of  the  hollow  which  will 
cast  a shadow  on  the  spherical 
surface  inside.  The  points  of 
tangency  ay  and  hy  are  the  lim- 
its of  this  shade  line  aycyhy.  The  remaining  portion  of  the  line 
aydyhy  is  not  a shade  line  since  the  light  would  reach  the  spherical 
surface  adjacent  to  it  and  also  reach  the  plane  surface  on  the  other 
side  of  aydyhy  outside  the  spherical  hollow. 

We  must  now  cast  the  shadow  of  the  line  aycyhy  on  the  spher- 
ical surface  of  the  hollow,  and  having  no  ground  line,  (since  neither 
Lie  Y nor  the  H projection  of  the  spherical  hollow  is  a line,)  we 
use  auxiliary  planes. 

If  we  pass  through  the  spherical  hollow,  parallel  to  the  plane 


SHADES  AND  SHADOWS 


27 


of  the  line  acb  (in  this  case  parallel  to  Y)  an  auxiliary  plane  P, 
it  will  cut  on  the  spherical  surface  a line  of  intersection  xy\  in 
elevation  this  will  show  as  a circle  xvif , whose  diameter  is  oh- 
tained  from  the  line  xhyh  in  the  plan.  This  line  of  intersection 
will  show  in  plan  as  a straight  line,  xhyh. 

Cast  the  shadow  of  the  line  acb  on  this  auxiliary  plane  P. 
This  is  not  difficult  because  the  plane  P was  assumed  parallel  to 
acb9  and  in  this  particular  case,  a*cvbv  is  the  arc  of  a circle.  To 
cast  its  shadow  on  P it  is  only  necessary  to  cast  the  shadow  of  its 
center  <?v,  using  the  line  P as  a ground  line  and  to  draw  an  arc  of 
same  length  and  radius. 

We  thus  obtain  the  arc 
avscvsfc)S'  Th  is  is  the  sh  ad  - 
ow  of  the  shade  line  of  the 
object  on  the  auxiliary 
plane  P.  It  will  be  noted 
that  this  shadow  a^sc^sb^s 
crossed  the  line  of  inter- 
section, made  by  P with  the 
spherical  surface,  at  the  two 
points  mP  and  ri^.  In  plan 
these  points  would  be  mh 
and  nh  which  are  two  points 
in  the  required  shadow  on 
the  spherical  surface  for 
they  are  the  shadows  of  two 
points  in  the  shade  line 
acb  and  they  are  also  on 
the  surface  of  the  spherical 
hollow  since  they  are  on  the 
line  of  intersection  xy 
which  lies  in  that  spherical 
surface.  With  one  auxil- 
iary plane  we  thus  obtain  two  points  in  the  shadow  of  the  hollow. 

In  Fig.  30  a number  of  auxiliary  planes  have  been  used  to  obtain 
a sufficient  number  of  points,  1,  2,  3,  4,  etc.,  of  the  shadow,  to  war- 
rant its  outline  being  in  elevation  and  plan  with  accuracy.  The 
shadow  in  plan  is  determined  by  projection  from  the  shadow  in 
elevation,  which  is  found  first. 


FIG -30 


199 


28 


SHADES  AND  SHADOWS 


74.  The  separate  and  successive  steps  in  this  method  of 
determining  the  shadow  of  an  object  by  the  use  of  auxiliary  planes 
are  as  follows: 

1.  Determine  the  shade  line  by  applying  to  the  object  the 
projections  of  the  ray  of  light. 

2.  Pass  the  auxiliary  planes  through  the  object  parallel  to 
the  plane  of  the  shade  line. 

3.  Find  the  line  of  intersection  which  each  auxiliary  plane 
makes  with  the  object. 

4.  Cast  the  shadow  of  the  shade  line  on  each  of  the  auxiliary 
planes. 

5.  Determine  the  point  or  points  where  the  shadow  on  each 
auxiliary  plane  crosses  the  line  of  intersection  made  by  that  plane 
with  the  object. 

G.  Draw  a line  through  these  points  to  obtain  the  required 
shadow. 

75.  Problem  XIV.  To  find  the  shadow  on  the  surface  of  a 
scotia. 

This  problem  is  similar  in  method  and  principle  to  that  for 
finding  the  shadow  of  a spherical  hollow.  Neither  the  Hor  Y pro- 
jection of  the  surface  of  the  scotia  is  a line,  and  we  therefore  must 
resort  to  some  method  other  than  that  generally  used.  The  follow- 
ing; is  the  most  accurate  and  convenient  although  the  shadow  can 
be  found  by  a method  to  be  explained  in  the  next  problem. 

76.  As  in  any  problem  in  shades  and  shadows,  the  first  step 
is  to  determine  the  shade  line. 

The  scotia  is  bounded  above  and  below  by  fillets  which  are 
portions  of  right  cylinders.  The  shadow  of  the  scotia  is  formed 
by  the  shadow  of  the  upper  fillet  or  right  cylinder  upon  the  sur- 
face of  the  scotia.  We  determine  the  shade  lines  of  the  cylinder, 
Problem  XI,  by  applying  to  the  plan  the  projections  of  the  ray, 
Fig.  31.  These  determine  the  shade  elements  at  and  and 
also  the  portion  of  the  perimeter  of  the  fillet,  xhahyh,  which  is 
to  cast  the  shadow  on  the  scotia. 

In  this  case,  as  in  most  scotias,  the  shadow  of  the  shade  ele- 
ments of  the  cylinder  falls  not  on  the  scotia  itself,  but  beyond  on 
the  II  or  Y plane,  or  some  other  object,  hence  we  can  neglect  them 
for  the  present. 


200 


SHADES  AND  SHADOWS 


29 


Having  determined  the  shade  line,  there  is  another  prelim- 
inary step  to  be  taken  before  finding  its  shadow.  That  is,  to  deter- 
mine  the  highest  point  in  the  shadow  ays.  We  do  this  to  know 
where  it  is  useless  to  pass  auxiliary  planes  through  the  scotia. 
Such  planes  would  evidently  be  useless  between  the  point  ays  and 
the  shade  line  xyay//y  in  elevation.  Also  because  we  could  not 
be  sure  that  in  passing  the  auxiliary  planes  we  were  passing  a 
plane  which  would  determine  this  highest  point. 

The  highest  point  of  shad- 
ow ays  is  determined,  there-  FlG^l 

fore,  as  follows: 

The  point  ah , lying  on  the 
diagonal  Peh  is  evidently 
the  point  in  the  shade  line 
which  will  cast  the  hicrhest 
point  in  the  shadow,  for,  con- 
sidering points  in  the  shade 
line  on  either  side  of  ah , it 
will  become  evident  that  the 
rays  through  them  must  in- 
tersect the  scotia  surface  at 
points  lower  down  than  the 
point  ays. 

The  point  a lies  in  a plane 
of  light  P,  which  passes 
through  the  axis  oh  of  the 
scotia.  This  plane,  therefore, 
cuts  out  of  the  scotia  surface 
a line  of  intersection  exactly  like  the  profile  aycy.  If  we  revolve 
the  plane  P and  its  line  of  intersection  about  the  axis  oh  until 
it  is  parallel  to  V,  the  line  of  intersection  will  then  coincide  with 
this  profile  aycy,  the  point  ay  having  moved  to  the  point  a'y . 

If,  before  revolving,  we  had  drawn  the  projections  of  the  ray 
of  light,  Pv,  through  the  point  ay,  they  would  be  the  lines  ayhy 
and  ahhh.  After  the  revolution  of  the  plane  P these  projections 
of  the  ray  are  the  lines  a'yhy  and  a'hhh.  The  point  h , being  in 
the  axis,  does  not  move  in  the  revolution  of  the  plane  P.  Th^ 
point  ays , the  intersection  of  the  projection  of  the'  ray  IIV  with 


201 


30 


SHADES  AND  SHADOWS 


the  profile  aycc , indicates  that  the  ray  R>  has  pierced  the  scotia 
surface.  If  now  the  plane  P is  revolved  back  to  its  original  posi- 
tion, this  point  a'vs  will  move  in  a horizontal  line  in  elevation  to 
the  point  ays,  and  the  point  ays  thus  obtained  is  the  shadow  of  the 
point  aY  on  the  surface  of  the  scotia  and  is  also  the  highest  point 
of  the  shadow. 


FIG>32 


77.  The  remainder  of  the  process  is,  from  now  on,  similar 
to  the  method  just  explained  in  the  previous  problem.  See  Fig.  32. 

We  pass  auxiliary  planes,  A,  B,  C,  etc.,  (in  this  case  parallel 
to  IT)  through  the  scotia. 

We  determine  in  plan  their  respective  lines  of  intersection 
with  the  scotia:  they  will  be  circles. 

Cast  the  shadow  of  the  arc  xhahyh  on  each  of  these  auxiliary 
planes.  This  is  done  by  casting  the  shadow  of  its  center  O and 
drawing  arcs  equal  to  xhahyh. 


202 


SHADES  AND  SHADOWS 


31 


The  points  of  intersection,  2h,  3h,  4h,  5h,  6h,  etc.,  are  points 
in  the  required  shadow  in  plan.  The  points  lh  and  10h  are  the  ends, 
where  the  shadow  leaves  the  scotia,  and  these  are  determined  by  tak- 
ing one  of  the  auxiliary  planes  at  the  line  MX.  The  points  lv,  2V, 
3V,  etc.,  are  obtained  in  the  elevation  by  projection  from  the  plan. 

The  shade  of  the  lower  fillet  is  determined  by  Problem  XI. 

78.  In  case  the  fillets  are  conical  instead  of  cylindrical  sur. 
faces,  as  is  sometimes  the  case 
in  the  bases  of  columns  where 
the  scotia  moulding  is  most 
commonly  found,  care  must 
be  taken  to  first  determine  the 
shade  elements  of  the  conical 
surface.  This  supposition  of 
conical  surfaces  wTould  mean 
a larger  arc  for  the  shade  line 
than  the  arc  xhahyh. 

U5E  OF  PLANES  OF  LIGHT 

PERPENDICULAR  TO 
THE  COORDINATE 
PLANES. 

79.  Another  method  often 
necessary  and  convenient  in 
casting  the  shadows  of  double- 
curved  surfaces  is  the  use  of 
yjlanes  of  light  perpendicular 
to  the  co-ordinate  plagues. 

These  auxiliary  planes  of 
light  are  passed  through  the 
given  object.  They  will  cut 
out  lines  of  intersection  with  the  object  and  to  these  lines  of  inter- 
section can  be  applied  the  projections  of  the  rays  of  light  which  lie 
in  the  auxiliary  planes  of  light.  The  points  of  contact  or  tangency, 
as  the  case  may  be,  of  the  projections  of  the  rays  and  the  line  of 
intersection  are  points  in  the  required  shadow. 

80.  The  use  of  this  method  will  be  illustrated  by  finding 
the  shadow  of  a sphere  in  the  following  problem.  The  shadow  of 
the  sphere  serves  to  illustrate  this  method  well,  but  a more  aceur- 


FIGA33 


203 


32 


SHADES  AND  SHADOWS 


ate  and  convenient  method  is  given  later  in  Problem  XXIX  for 
determining  the  shade  line  of  the  sphere  and  its  shadow. 

81.  Problem  XV.  To  find  the  shade  line  of  a sphere. 

In  Fig.  33  is  shown  the  plan  and  elevation  of  a sphere. 
Through  the  sphere  in  plan,  pass  the  auxiliary  jplane  of  light  P, 
perpendicular  to  H.  This  cuts  out  of  the  sphere  the  ‘‘line  of  in- 
tersection,” shown  in  the  elevation.  This  “line  of  intersection”  is 
determined  by  using  the  auxiliary  planes  A,  B,  C,  D,  etc.,  each 

To  this  line  of  intersection 
made  by  the  plane  of  light 


plane  giving  two  points  in  the  line. 

PIG434 


r 

^ -L—A 

i 

V- 

) 

A 

i 

\ 

1 

<f  1 

r 

! 

1 JmM.  \ 

v 

K 

P 

c- 

a| 

'*/  \\  N 

4*5 

B1 


A- 


i i 


A 


P,  with  the  sphere,  we  apply 
the  projections  of  the  ray  and 
obtain  two  points,  xYyY,  in 
the  required  shade  line.  Other 
points  can  be  determined  by 
using;  a number  of  these 

O 

planes  of  light,  as  shown  in 
Fig.  34,  P,  Q,  H and  S. 

The  points  xY  and  if  can  be 
projected  to  the  plan  to  deter- 
mine the  shade  line  there. 
The  ends  of  the  major  axis 
of  the  ellipse  aY  and  hY  are  de- 
termined by  applying  directly 
to  the  sphere  the  projections 
of  the  ray.  The  same  is  true 
of  the  plan. 

82.  ^Problem  XVI.  To 
find  the  shadow  of  pediment 
mouldings. 

Fig.  35  shows  a series  of 
pediment  mouldings  in  elevation,  the  mouldings  being  supposed  to 
extend  to  the  left  and  right  indefinitely.  At  the  left  is  a “Bight  Sec- 
tion,” showing  the  profile  of  each  moulding  forming  the  pediment. 

The  shadow  of  such  an  object  can  be  most  conveniently  found 
by  the  use  of  a plane  of  light  perpendicular  to  the  V plane  and 

intersecting  the  mouldings. 

© © 

^Optional. 


U4 


~N 


\ 


204 


SHADES  AND  SHADOWS 


83 


If  such  a “ Plane  of  Light  ” (45°  line)  as  that  shown  in  Fig.  35 
is  passed  through  the  mouldings,  it  will  be  evident  that  this  plane 
will  cut  the  mouldings  along  a line  of  intersection  which  can  be 
made  use  of  in  determining  the  shadow  of  each  moulding  upon  the 
others.  If  we  find  the  profile  projection  of  this  line  of  intersec- 
tion using  the  right  section,  we  can  apply  the  profile  projections 
of  rays  of  light  to  the  line  of  intersection.  It  will  then  be 
evident  what  faces  the  light  strikes  directly  and  to  what  edges  the 
rays  are  tangent. 

The  line  of  intersection  in  Fig.  35  made  by  the  Plane  of  Light 


is  shown  in  vertical  projection  by  the  45°  line  aylycydy,  etc.  The 
profile  uvbv&\dv^  etc.,  is  the  profile  projection  of  this  line  of  intersec- 
tion; the  point  R is  evidently  on  a horizontal  line  to  the  left  of 
the  point  ay  at  a distance  from  the  line  Vp  ( profile  projection 
of  V)  equal  to  ab\  obtained  from  the  Right  Section.  In  the 
same  way  the  point  cv  is  on  a horizontal  line  to  the  left  of  cy  and 
at  a distance  from  the  line  Vp  equal  to  the  distance  cf  also  ob- 
tained from  the  Right  Section.  In  a similar  manner  the  other 
points  in  the  profile  projection  are  found.  The  vertical  line  Rcv 
is  the  profile  projection  of  the  line  of  intersection  which  the  Plane 
of  Light  makes  with  the  fillet,  this  line  in  direct  elevation  is  bycy. 

If  we  now  apply  to  this  profile  projection  of  the  line  of  inter- 
section the  profile  projections  of  the  ray  (45°  lines)  we  see  that  the 


34 


SHADES  AND  SHADOWS 


fillet  &p6>p  is  in  tlie  light,  and  that  the  ray  is  tangent  to  its  lower 
edge  <?p.  We  also  see  that  this  tangent  ray  strikes  the  face  D at 
the  point  Zp;  this  means  that  the  shadow  of  the  edge  c falls  upon 
the  face  D.  Since  the  mouldings  of  the  pediment  are  all  parallel 
to  each  other,  the  edge  c is  parallel  to  the  face  D,  therefore,  (30) 
the  shadow  of  c on  D will  he  parallel  to  0 itself.  This  shadow  is 
found  in  the  elevation  by  drawing  a horizontal  line  from  the  point 
/p  back  to  the  Plane  of  Light . This  operation  gives  the  point  lv 
and  we  draw  through  the  point  lv  a line  parallel  to  the  edge  C,  as 
a part  of  the  required  shadow.  Evidently  that  portion  of  the  ele- 
vation between  the  edge  C and  its  shadow  will  be  in  shadow. 

In  a like  manner  the  edge  cZp  is  found  to  cast  its  shadow  on 
the  plane  V,  below  the  pediment  mouldings  proper,  and  its  shadow 
is  of  course  a line  drawn  through  2V  parallel  to  the  lines  of  the 
mouldings. 

o 

To  return  to  the  shadow  of  the  edge  C on  the  face  D.  It  will 
be  noticed  that,  if  this  is  extended  far  enough,  it  will  cross  the 
pediment  mouldings  on  the  right-hand  slope;  as  these  are  not 
parallel  to  the  edge  C,  the  shadow  on  them  will  not  be  a parallel 
line  and  we  must  ’use  a separate,  though  similar,  method  for  deter- 
mining this  portion  of.  the  shadow. 

If  auxiliary  planes  O,  Q and  P.  parallel  to  V are  passed 
through  the  crowning  moulding,  they  will  cut  out  of  it  lines  of 
intersection  wdiich  will  be  parallel  to  the  other  lines  of  the  pedi- 
ment. (See  the  enlarged  diagram  at  A showing  the  line  of  inter- 
section of  the  auxiliary  plane  O.) 

If  we  cast  the  shadow  of  the  edge  C on  this  plane  O,  by  draw- 
ing the  45°  line  from  cp  to  the  line  PO  (the  profile  projection  of 
O)  and  from  the  point  4p  draw  a horizontal  line  back  to  the  Plane 
of  Light,  we  shall  obtain  the  line  O (see  “shadow  on  PO”  in  dia- 
gram A).  This  shadow  will  cross  the  Line  of  intersection  of 
PO  at  the  point  5V.  The  point  5V  will  be  one  point  in  the  shadow 
of  the  edge  C (indefinitely  extended)  on  the  right-hand  slope  of 
the  pediment.  Other  points,  8V  and  9V,  can  be  found  in  a like 
manner  by  use  of  the  auxiliary  planes  Q and  P.  Through  a suffi- 
cient number  of  these  points  the  curve  5V9V8V  is  drawn.  This  curve 
is  the  required  shadow.  The  shadow  of  the  end  of  the  edge  C is 
found  by  drawing  a 45°  line  from  the  point  mv  (diagram  A)  to  the 


206 


FIG"  35 


36 


SHADES  AND  SHADOWS 


curve.  The  point  of  intersection,  10v,  is  the  shadow  of  the  end  of 
the  edge  C.  It  is  also  the  beginning  of  the  shadow  of  the  edge  B 
on  the  right-hand  slope,  which  shadow  is  parallel  to  B. 

The  remaining  shadows  of  the  pediment  are  found  in  the 
same  manner,  and  may  be  understood,  from  the  diagram,  without 
a detailed  explanation. 

SHORT  METHODS  OF  CONSTRUCTION. 

83.  The  following  problems  illustrate  short  and  convenient 
methods  of  construction  for  determining  the  shadows  of  lines,  sur- 
faces  and  solids,  in  the  positions  in  which  they  commonly  occur 


in  architectural  drawings.  These  methods  here  worked  out  with 
regard  to  the  co-ordinate  planes  apply  also  to  parallel  planes. 

84.  They  will  be  found  to  be  of  great  assistance  in  casting 
the  shadows  in  architectural  drawings.  The  latter  seldom  have 
the  plan  and  elevation  on  the  same  sheet,  and  these  methods  have 
been  devised  to  enable  the  shadows  to  be  cast  on  the  elevation 
without  using  construction  lines  on  the  plan  or  profile  projection. 
Such  distances  as  are  needed  and  obtained  from  the  plan,  can  be 
taken  by  the  dividers  and  applied  to  the  construction  in  the  elevation. 

In  casting  shadows  it  will  be  found  convenient  to  have  a tri- 
angle,  one  of  whose  angles  is  equal  to  the  true  angle  which  the  ray 
of  light  makes  with  the  co-ordinate  plane.  See  Fig.  36.  With 
such  a triangle  the  revolved  position  of  the  ray  of  light  can  be 
drawn  immediately  without  going  through  the  operation  of  revolv- 
ing the  ray  parallel  to  one  of  the  co-ordinate  planes. 

85.  Problem  XVII.  To  construct  the  shadow  on  a co=ordi= 
nate  plane  of  a point. 


208 


SHADES  AND  SHADOWS 


37 


It  will  lie  on  the  45°  line  passing  through,  the  point  and  rep- 
resenting the  projection  of  the  ray  of  light  on  that  plane.  It  will 
be  situated  on  the  45°  line  at  a distance  from  the  given  point, 
equal  to  the  diagonal  of  a square,  the  side  of  which  is  equal  to  the 
distance  of  the  point  from  the  plane. 

Given  the  vertical  projection  of  the  point  a situated  2 inches 
from  the  Y plane,  to  construct  its  shadow  on  Y.  Fig.  37. 

From  the  point  ay  draw  the  45° 
degree  line  ayay 3 equal  in  length 
to  the  diagonal  of  a square  whose 


sides  measure  2 inches.  Then  avs 
is  the  required  shadow. 

86.  Problem  XVIII.  To  con= 
struct  the  shadow  of  a line  perpendicular  to  one  of  the  coordi- 
nate planes. 

(1)  It  will  coincide  in  direction  with  the  projection  of  the 
ray  of  light  upon  that  plane,  without  regard  to  the  nature  of  the 
surface  upon  which  it  falls. 


FIG-4-1 


(2)  The  length  of  its  projection  upon  that  plane  will  be 
equal  to  the  diagonal  of  a square,  of  which  the  given  line  is  one  side. 
Given  the  vertical  projection  of  the  line  ab  perpendicular  to 


£09 


88 


SHADES  AND  SHADOWS 


V,  2 inches  long  and  \ inch  from  V,  to  construct  its  shadow  on 
V.  See  Fig.  38.  Find  the  shadow  of  the  point  aY  by  Problem 
XVII. 

From  the  point  aYS  draw  the  45°  line  aYsbYS  equal  to  the  diag- 
onal of  a square  2. inches  on  each  side. 

86.  Problem  XIX.  To  construct  the  shadow  of  a line  on  a 
plane  to  which  it  is  parallel. 

(1)  It  will  be  parallel 
to  the  projection  of  the 
given  line. 

(2)  It  will  be  equal  in 
length  to  the  projection  of 
the  line. 

Given  the  vertical  pro- 
jection of  the  line  ah , par- 
allel to  Y,  2 inches  in 
length  and  4 inch  from  Y, 
to  construct  its  shadow  on 
Y.  See  Fig.  89. 

Find  the  shadow  of  aY 
by  Problem  XVII. 

Draw  aYSbYS  parallel  and 
equal  in  length  aYbY. 

87.  Problem  XX.  To 
construct  the  shadow  of  a 
vertical  line  on  an  in= 
dined  plane  parallel  to 
the  ground  line. 

It  makes  an  angle  with 
the  horizontal  equal  to  the 
angle  which  the  given  plane  makes  with  H. 

Given  the  vertical  projection  of  a vertical  line  ab , its  lower 
end  resting  on  a plane  parallel  to  the  ground  line  and  making  an 
angle  of  30°  with  H,  to  construct  its  shadow  on  this  inclined  plane. 
See  Fig.  40.  Through  the  point  bY  draw  the  30°  line  bYaYS.  The 
point  aYS , the  end  of  the  shadow,  is  determined  by  the  intersection 
of  the  45°  line  drawn  through  the  end  of  the  line  aY. 

88.  Problem  XXI.  To  construct  the  shadow  on  a coordi- 
nate plane  of  a plane  which  is  parallel  to  it. 


SHADES  AND  SHAD O AYS 


39 


(1)  It  will  be  of  the  same  form  as  that  of  the  given  surface. 

(2)  It  will  be  of  the  same  area. 

If  the  plane  surface  is  a circle,  the  shadow  can  be  found  by 
finding  the  shadow  of  its  center,  by  Problem  XVII,  and  with  that 
as  a center  describing  a circle  of  the  same  radius  as  the  given  circle. 

Given  a plane  parallel  to  Y,  -J  inch  from  Y and  14  inches 
square,  to  construct  its  shadow  on  Y.  See  Fig.  41. 

Find  the  shadow  of  any  point  ay  for  example,  by  Problem 
2" 

~ F\  ‘ 


XYII.  On  that  point  of  the  shadow  construct  a similar  square 
whose  side  equals  14  inches. 

89.  Problem  XXII.  To  construct  the  shadow  on  V of  a 
circular  plane  which  is  parallel  to  H,  or  which  lies  in  a profile 
plane. 

Given  avoyby,  the  projection  of  a circular  plane  perpendicular 
to  Y and  H,  2 inches  in  diameter,  its  center  being  2^  inches  from 
Y,  to  construct  the  shadow  on  Y.  Fig.  42.  The  shadow  of  ov, 
the  center  of  the  circular  plane  is  found  by  Problem  XYII.  About 
ovs  as  a center,  construct  the  parallelogram  ABCD  made  up  of 
the  two  right  triangles  ADB  and  DBG,  the  sides  adjacent  to  the 
right  angles  being  equal  in  length  to  the  diameter,  2 inches,  of 
the  circular  plane.  Draw  the  diameters  and  diagonals  of  this  par- 
allelogram. The  diameter  TAY  is  equal  to  the  diameter  of  the 
given  circle  and  parallel  to  it. 

AYith  oys  as  a center  and  OD  and  OB  as  radii,  describe  the 
arcs  cutting  the  major  diameter  of  the  parallelogram  in  the  points 


40 


SHADES  A AD  SHADOWS 


E and  F.  Through  E and  E draw  lines  parallel  to  the  short  diam- 
eter, cutting  the  diagonals  in  the  points  G,  H,  M and  N.  These 
last  four  points  and  the  extremities  of  the  diameters  E,  S,  T,  and 
W,  are  eight  points  in  the  ellipse  which  is  the  shadow  of  the  given 
circular  plane  on  Y.  A similar  construction  is  followed  for  find- 
ing the  shadow  on  Y of  a circular  plane  parallel  to  H.  Fig.  43. 

90.  Problem  XX5H.  To  construct  the  shade  line  of  a cylin= 
der  whose  axis  is  perpendicular  or  parallel  to  the  ground  line. 

Given  the  elevation  of  a cylinder,  its  axis  being  AB  perpen- 
dicular to  II.  To  construct  shade  lines.  Fig-.  44. 

o 

Let  CD  be  any  horizontal  line 
drawn  through  the  cylinder. 

Construct  the  45°  isosceles  tri- 
angle AGD  on  the  right  half  of 
the  diameter. 

With  the  radius  AG  describe  the 

semi-circular  arc  rnG'/i,  cutting  the 

7 . & c 

horizontal  line  CD  in  the  points  m 
and  n. 

These  two  points  will  determine 
the  shade  elements  mo  and  njp. 

91.  Problem  XXIV.  To  con= 
struct  the  shadow  on  a plane 
(parallel  to  its  axis)  of  a circular 
cylinder  whose  axis  is  either  perpendicular,  or  parallel  to  the 
ground  line. 

Let  cl = the  distance,  in  the  elevation,  between  the  projection 
of  the  axis  of  the  cylinder  and  the  projection  of  the  visible  shade 
element.  Let  Z»=the  distance  between  the  axis  of  the  cylinder 
and  the  plane  on  which  the  shadow  falls,  to  be  obtained  from  the 
plan. 

Then  the  distance,  between  the  visible  shade  element  and  its 
shadow  on  the  given  plane,  will  be  equal  to  a-\-b. 

The  vudth  of  the  shadow  on  the  given  plane  will  be  equal  to  4 a. 

Given  the  circular  cylinder  CDEF  (Fig.  45),  its  axis  AB  per- 
pendicular to  H.  To  construct  its  shadow  on  the  Y plane  which 
is  1J  inches  distant  from  the  axis  AB.  The  shade  elements  mo 
and  np  can  be  constructed  by  Problem  XXIII.  Draw  ES  the 


212 


SHADES  AND  SHADOWS 


41 


shadow  of  the  shade  element  np,  parallel  to  up,  and  distant  from 
it  a + 14  inches.  The  width  of  the  shadow  on  the  given  plane  will 

F1G*45  ^ ^mes  distance 

An. 

92.  Problem  XXV. 
To  construct  the  shadow 
on  a right  cylinder  of  a 
horizontal  line. 

a.  It  will  be  the  arc 
of  a circle  of  the  same 
radius  as  that  of  the  cyl- 
inder. 

b.  The  center  of  the 
circle  will  be  on  the  axis 
of  the  cylinder  as  far  be- 


low the  given  line  as  that 

O 

line  is  in  front  of  the 


axis. 

G 


iven  a right  circular 

O 


cylinder  CDEF,  whose  diameter  is  1|  inches,  and  a horizontal  line 
ah,  1^  inches  in  front  of  the  axis  of  the  cylinder.  To  construct 
the  shadow.  Eig.  46. 


F1G"46 


F B E 


Locate  the  point  o on 


$ 


\ FIG -4  J 

\ 

\ 


the  axis  1J  inches  below  ayh\  With 


213 


42 


SHADES  AND  SHADOWS 


o as  a center,  and  radius  equal  to  inch  describe  the  arc  mnp , the 
required  shadow. 

93.  Problem  XXVI.  To  con  - 
struct  the  shadow  of  a verti- 
cal  line  on  a series  of  mould- 
ings which  are  parallel  to  the 
ground  line. 

The  shadow  reproduces  the 
actual  profile  of  the  mouldings. 

Given  a vertical  line  aYbY 
which  casts  a shadow  on  the 
moulding  M,  which  is  parallel 
to  the  ground  line,  and  whose 
profile  is  shown  in  the  section 
ABCD.  The  line  aybY,  is  1 inch 
in  front  of  the  fillet  AB.  To 
construct  its  shadow,  Fig.  47: 

Construct  the  shadow  on  the  fillet  AB,  of  the  end  of  the  line 
aY,  or  any  other  convenient  point  in  the  line,  by  Problem  XVII. 

From  the  point  as  the 
shadow  of  the  line  repro- 
duces the  profile  ABCD 
and  we  obtain  asnsosbs , 
the  required  shadow. 

94.  Problem  XXVII. 
To  construct  the  shad= 
ow  on  the  intrados  of  a 
circular  arch  in  section, 
the  plane  of  the  arch 
being  in  profile  projec- 
tion. 

Let  AB  (Fig.  48)  be 
the  “springing  line”  of 
the  arch.  Let  CD  be 
the  radius  of  the  curve. 
The  point  F is  determined  by  the  construction  used  in  finding 
the  shade  element  of  a cylinder.  Problem  XXIII.  At  the  point 
F draw  the  line  GII,  with  an  inclination  to  the  “horizontal”  of  1 
in  2.  Through  the  point  D draw  the  45°  line  DB.  The  curve  of 


FIG-48 


214 


SHADES  AND  SHADOWS 


43 


the  line  of  shadow  will  be  tangent  to  these  two  lines  at  the  points 
F and  B.  The  required  shadow  is  that  portion  of  the  curve  be- 
tween the  lines  DC  and  MN. 

A similar  construction  is  used  in  the  case  of  a hollow  semi- 
cylinder when  its  axis  is  vertical,  except,  that  the  line  Oil  has  then 
an  inclination  to  “the  horizontal”  of  2 in  1.  Fie-.  49. 

95.  Problem  XXVIII.  To  construct  the  shadow  of  a spheri= 
cal  hollow  with  the  plane  of  its  face  parallel  to  either  of  the 
coordinate  planes. 

The  line  of  shadow  is  a semi-ellipse.  The  projections  of  the 
rays  of  light  tangent  to  the  circle  determine  the  major  axis.  The 
semi  minor  axis  is  equal  to  J the  radius  of  the  circle. 

Given  the  vertical  projection  of  a spherical  hollow,  the  plane 
of  its  face  parallel  to  V.  Fig.  50. 

Determine  the  ends  of  the  major  axis  by  drawing  the  pro- 
jections of  the  rays  of  light  tangent  to  the  hollow.  The  semi- 
minor axis,  oci , equals  J the  radius 
ob.  On  be  and  oa  construct  the 
semi -ellipse,  the  required  shadow. 

96.  Problem  XXIX.  To  con= 
struct  the  shade  line  and  shadow 
of  a sphere.  Fig.  5i. 

Let  the  circle  whose  center  is  o 
be  the  vertical  projection  of  a 
sphere  whose  center  is  at  a dis- 
tance x from  the  V plane. 

The  shade  line  will  be  an  ellipse. 
The  major  axis  of  this  ell ij^se  is  de- 
termined by  the  projections  of  the  rays  of  light  tangent  to  the 
circle.  The  semi  minor  axis  and  two  other  points  can  be  deter- 
mined as  follows  : 

Through  the  points,  A,  <9,  and  B,  draw  vertical  and  horizon- 
tal lines,  intersecting  in  the  points  E and  D. 

The  points  E and  D are  two  points  in  the  required  shade  line. 

Through  the  point  E draw  the  45°  line  EE.  Through  the 
point  F,  where  this  line  intersects  the  circle,  and  the  point  B,  draw 
the  line  FB.  The  point  C,  where  this  line  EB  intersects  the  45 3 
line  through  the  center  of  the  sphere,  o , is  the  end  of  the  semi- 


FIG<50 


215 


44 


SHADES  AND  SHADOWS 


minor  axis.  The  shadow  of  the  sphere  on  the  co-ordinate  plane  will 
also  be  an  ellipse.  The  center  of  this  ellipse,  os , will  be  the  shadow 
of  the  center  of  the  sphere.  It  will  be  determined  by  Problem 
XVII.  The  ends  of  the  major  axis  MX,  will  be  on  the  projection  of 
the  ray  of  light  drawn  through  the  center  of  the  sphere.  The  minor 
axis  PR  will  be  a line  at  right  angles  to  this  through  the  point  os. 
Its  length  will  be  determined  by  the  projections  of  the  rays  of 


light  BR  and  AP  tangent  to  the  circle,  and  is  equal  to  the  diameter 
of  the  sphere.  The  points  M and  N,  which  determine  the  ends  of 
the  major  axis,  are  the  apexes  of  equilateral  triangles  PMR  and 
PNR,  constructed  on  the  minor  axis  as  a base. 

97.  Problem  XXX.  To  construct  the  shade  line  of  a torus. 

Fig.  52,  in  elevation:  The  points  1 and  5 can  be  determined 

by  drawing  the  projections  of  the  rays  of  light  tangent  to  the  ele- 
vation. Since  the  shade  line  is  symmetrical  on  either  side  of  the 
line  MN  in  plan,  the  points  3 and  7 can  be  found  from  1 and  5,  by 
drawing  horizontal  lines  to  the  axis.  The  points  4 and  8 are 


SHADES  AXD  SHADOWS 


45 


determined  by  the  construction  used  in  finding  the  shade  elements 
of  a cylinder.  Problem  XXIII. 

The  above  points  can  be  determined  without  the  use  of  plan. 


FIG-  52 


The  highest  and  lowest  points  in  the  shade  line,  2 and  G,  can 
be  found  only  by  use  of  plan.  It  is  not  necessary,  as  a rule,  to 
determine  accurately  points  2 and  G.  The  shade  line  in  plan  will 
be,  approximately,  an  ellipse  whose  center  is  o.  The  ends  of  the 
major  axis  E and  S,  are  determined  by  the  projections  of  the  rays 
of  light  tangent  to  the  circle.  Other  points  can  be  determined 
without  the  use  of  the  elevation  as  follows:  With  center  o , con- 

struct the  plan  of  a sphere  whose  diameter  equals  that  of  the  circle 
which  generated  the  torus.  Determine  the  shade  line  by  Problem 
XXIX.  Draw  any  number  of  radii  OE,  OF,  OG,  etc. 

On  these  radii,  from  the  points  where  they  intersect  the  shade 
line  of  the  sphere,  lay  off  the  distance  ET,  giving  the  points 
c,f  and  (j.  These  are  points  on  the  required  shade  line. 


217 


EXAMINATION  PAPER 


TOWER  CONVERSE  MEMORIAL  LIBRARY,  MALDEN,  MASS, 

H.  H.  Richardson,  Architect. 

Note  treatment  of  shadows  in  a perspective  drawing. 


Note.— The  problems  are  to  be  worked  out  on  the  plates  accompanying 
the  Instruction  Paper,  and  outlines  are  not  to  be  redrawn , 


SHADES  AND  SHADOWS. 

% 

EXAMINATION  PLATES. 

98.  General  Directions.  Plates  are  to  be  drawn  in  pencil. 

Show  distinctly  and  leave  all  construction  lines. 

Shadows  are  to  be  cross-hatched  lightly,  and  their  outline 
drawn  with  a distinct  1>1  ack  line. 

PLATE  I. 

99.  See  directions  on  plate. 

PLATE  II. 

100.  Find  the  shadows  of  lines  ah,  etc.,  in  Problems  XIV. 
XVI. 

101.  In  Problem  XVII  find  the  shadow  of  line  ah  on  the 
planes  A,  B,  and  C. 

102.  In  Problem  XVIII  find  the  shadow  cf  plane  abed. 

PLATE  III. 

103.  See  directions  on  plate. 

PLATE  IV. 

101.  See  directions  on  plate. 

PLATE  V. 

105.  In  Problem  XXV  find  all  the  shadows  on  the  steps 
and  the  shadows  on  the  co-ordinate  planes  in  plan  and  elevation. 
Letter  carefully  the  various  planes  in  elevation  and  plan. 

106.  In  Problem  XXVI  find  all  the  shades  and  shadows  of 
the  cylinder  and  its  shadows  on  the  co-ordinate  planes. 

PLATE  VI. 

107.  In  Problems  XXVIII  and  XXIX  find  the  shades  and 
shadows  of  objects  and  their  shadows  on  the  co-ordinate  planes. 

108.  In  Problem  XXX,  C is  a square  projection  or  fillet  on 
the  V plane.  Below  this  fillet  and  also  applied  to  the  V plane 
are  portions  of  two  cylinders,  DD,  which  support  the  fillet  C. 
Find  the  shades  and  shadows  in  elevation  only. 


48 


SHADES  AND  SHADOWS 


PLATE  VII. 

109.  Problem  XXXI,  given  a spherical  hollow,  its  plane 
parallel  to  Y,  find  its  shadow. 

110.  Problem  XXXII,  given  a scotia  moulding,  the  upper 
fillet  of  which  is  the  frustum  of  a cone,  the  lower  fillet  is  a cylin- 
der. Find  its  shadow  in  elevation  and  plan. 

* PLATE  VIII, 

112.  Problem  XXXIII  shows  a series  of  pediment  mould- 
ings applied  to  a vertical  wall  A.  Find  the  shadows  on  the  mould- 
ings and  the  shadows  of  the  mouldings  on  the  vertical  plane  A. 

PLATE  IX. 

113.  In  Problem  XXXIY  find  the  shadows  of  a given 
window. 

114.  In  Problem  XXXY  find  the  shadows  of  the  given  key- 
block  and  the  shadow  of  the  keyblock  on  the  vertical  wall  to  which 
it  is  applied.  Use  the  short  methods  of  construction  and  use  the 
plan  only  from  which  to  take  distances. 

PLATE  X. 

115.  Problem  XXXVI.  Given  the  upper  portion  of  a Doric 
order,  the  column  being  engaged  to  the  vertical  wall  Y,  see  plan. 
The  entablature  breaks  out  over  the  column,  see  plan.  Find  all 
the  shadows,  using  the  short  methods  of  construction  and  use  the 
plan  only  to  obtain  required  distances. 

PLATE  XL 

116.  Problem  XXXVII.  Given  a rectangular  niche,  as 
shown  by  the  plan,  having  a circular  head  as  shown  by  the  eleva- 
tion. Situated  in  the  niche  is  a pedestal  in  the  form  of  truncated 
square  pyramid.  This  pedestal  has  on  its  four  side  faces  projections 
as  shown  in  the  elevation  and  plan.  On  the  pedestal  rests  a sphere. 
Find  all  the  visible  shadows  in  the  elevation.  Use  the  short  methods 
of  construction  and  use  the  plan  only  for  determining  distances. 

117.  Problem  XXXVIII.  Given  a niche  in  the  form  of  a 
spherical  hollow.  The  profile  of  the  architrave  mouldings  is  shown 
at  A.  Find  all  the  shadows.  Use  the  short  methods  of  construction. 

PLATE  XII. 

118.  Problem  XXXIX.  Given  the  lower  part  of  a column 
standing  free  from  a vertical  wall,  and  resting  on  a large  square 
base,  the  base  having  a moulded  panel  in  its  front  face.  At  the  foot 
of  the  vertical  wall  is  a series  of  base  mouldings,  the  lower  ones 
cutting  into  the  side  of  the  square  base  on  wThich  the  column  stands, 
see  plan.  Find  all  the  visible  shadows,  using  the  short  methods  of 
construction. 

* Optional. 


222 


SHADES  & SHADOWS 


PLATE  I 


~1 


DATE 


NAME 


SHADES  & SHADOWS 


PLATE  II 


rind  shade  of  objects  and  shadows  on  V and  H . 

•19-  -20- 


DATE 


NAJAE 


SHADES  & SHADOWS  PLATE  IV 


DATE,  NA7AE 


SHADES  &,  SHADOWS 


PLATE  V 


DATE 


NAME 


SHADES  &,  SHADOWS PLATE  VII 


DATE  NAME 


SHADES  & SHADOWS  PLATE  IX 


Kle vaXion  of  Side 

Key  block  ElevaJton 


SHADES  &,  SHADOWS PLATE  X 


DATE 


SHADES  &,  SHADOWS PLATE  XI 


DATE 


[ 


DATE  NA7AE 


/^IPf  Kdvf  rv  B v i Id  i y\$ 


A STUDY  IN  PEN  AND  INK  RENDERING 

(For  a different  treatment  of  the  same  build’iig,  see  page  406.) 


PERSPECTIVE  DRAWING 


DEFINITIONS  AND  GENERAL  THEORY. 

1.  AYhen  any  object  in  space  is  being  viewed,  rays  of  light 
are  reflected  from  all  points  of  its  visible  surface,  and  enter  the 
eye  of  the  observer.  These  rays  of  light  are  called  visual  rays. 
They  strike  upon  the  sensitive  membrane,  called  the  retina,  of 
the  eye,  and  form  an  image.  It  is  from  this  image  that  the 
observer  receives  his  impression  of  the  appearance  of  the  object 
at  which  he  is  looking. 

2.  In  Fig.  1,  let  the  triangular  card  abc  represent  any  object 
in  space.  The  image 
of  it  on  the  retina 
of  the  observer’s  eye 
will  be  formed  by 
the  visual  rays  re- 
flected from  its  sur- 
face. These  rays 
form  a pyramid  or 
cone  which  has  the  observer’s  eye  for  its  apex,  and  the  object  in 
space  for  its  base. 

3.  If  a transparent  plane  M,  Fig.  2,  be  placed  in  such  a 
position  that  it  will  intersect  the  cone  of  visual  rays  as  shown, 
the  intersection  will  be  a projection  of  the  object  upon  the  plane 
M.  It  will  be  noticed  that  the  projecting  lines,  or  projectors, 
instead  of  being  perpendicular  to  the  plane,  as  is  the  case  in 
orthographic  projection,*  are  the  visual  rays  which  all  converge  to 
a single  point  coincident  with  the  observer’s  eye. 

* In  orthographic  projection  an  object  is  represented  upon  two  planes  at  right  angles 
V*  each  other,  by  lines  drawn  perpendicular  to  these  planes  from  all  points  on  the  edges  or 
contour  of  the  object.  Such  perpendicular  lines  intersecting  the  planes  give  figures  which  are 
ailed  projections  ( orthographic ) of  the  object. 


a 


249 


4 


PERSPECTIVE  DRAWING. 


4.  Every  point  or  line  in  the  projection  on  the  plane  M will 
appear  to  the  observer  exactly  to  cover  the  corresponding  point  or 
line  in  the  object.  Thus  the  observer  sees  the  point  aY  in  the 
projection,  apparently  just  coincident  with  the  point  a in  the 
object.  This  must  evidently  be  so,  for  both  the  points  av  and  a 
lie  on  the  same  visual  ray.  In  the  same  way  the  line  avbv  in  the 
projection  must  appear  to  the  observer  to  exactly  cover  the  line 
ab  in  the  object ; and  the  projection,  as  a whole,  must  present  to 
him  exactly  the  same  appearance  as  the  object  in  space. 

5.  If  the  projection  is  supposed  to  be  permanently  fixed 

upon  the  plane,  the 
object  in  space  may 
be  removed  without 
affecting  the  image 
on  the  retina  of  the 
observer’s  eye,  since 
the  visual  rays  which 
were  originally  re- 
flected from  the  sur- 
face of  the  object 
are  now  reflected 
from  the  projection 
on  the  plane  M.  In 
other  words,  this 
projection  may  be 

used  as  a substitute  for  the  object  in  space,  and  when  placed  in 
proper  relation  to  the  eye  of  the  observer,  will  convey  to  him  an 
impression  exactly  similar  to  that  which  would  be  produced  were 
he  looking  at  the  real  object. 

6.  A projection  such  as  that  just  described  is  known  as  a 
perspective  projection  of  the  object  which  it  represents.  The 
plane  on  which  the  perspective  projection  is  made  is  called  the 
Picture  Plane.  The  position  of  the  observer’s  eye  is  called  the 
Station  Point,  or  Point  of  Sight. 

7.  It  will  be  seen  that  the  perspective  projection  of  any 
point  in  the  object,  is  where  the  visual  ray,  through  that  point, 
pierces  the  picture  plane. 

8.  A perspective  projection  may  be  defined  as  the  represen- 


250 


PERSPECTIVE  DRAWING. 


tation,  upon  a plane  surface,  of  the  appearance  of  objects  as  seen 
from  some  given  point  of  view. 

9.  Before  beginning  the  study  of  the  construction  of  the 
perspective  projection,  some  consideration  should  be  given  to 
phenomena  of  perspective.  One  of  the  most  important  of  these 
phenomena,  and  one  which  is  the  keynote  to  the  whole  science  of 
perspective,  has  been  noticed  by  everyone.  It  is  the  apparent 
diminution  in  the  size  of  an  object  as  the  distance  between  the 
object  and  the  eye  increases.  A railroad  train  moving  over  a 
long,  straight  track,  furnishes  a familiar  example  of  this.  As  the 
train  moves  farther  and  farther  away,  its  dimensions  apparently 
become  smaller  and  smaller,  the  details  grow  more  and  more 
indistinct,  until  the  whole  train  appears  like  a black  line  crawling 
over  the  ground.  It  will  be  noticed  also,  that  the  speed  of  the 
train  seems  to  diminish  as  it  moves  away,  for  the  equal  distances 
over  which  it  will  travel  in  a given  time,  seem  less  and  less  as 
they  are  taken  farther  and  farther  from  the  eye. 

10.  In  the  same  way,  if  several  objects  having  the  same 
dimensions  are  situated  at  different  distances  from  the  eye,  the 
nearest  one  appears  to 
be  the  largest,  and  the 
others  appear  to  be 
smaller  and  smaller  as 
they  are  farther  and 
farther  away.  Take, 
for  illustration,  a long,  b 
straight  row  of  street- 
lamps.  As  one  looks 
along  the  row,  each 
succeeding  lamp  is  ap- 
parently shorter  and  smaller  than  the  one  before.  The  reason  for 
this  can  easily  be  explained.  In  estimating  the  size  of  any  object, 
one  most  naturally  compares  it  with  some  other  object  as  a stand- 
ard or  unit.  Now,  as  the  observer  compares  the  lamp-posts,  one 
with  anothar,  the  result  will  be  something  as  follows  (see  Fig.  3). 
If  he  is  looking  at  the  top  of  No.  1,  along  the  line  ba , the  top  of 
No.  2 is  invisible.  It  is  apparently  below  the  top  of  No.  1,  for,  in 
order  to  see  No.  2,  he  has  to  lower  his  eye  until  he  is  looking  in 


251 


6 


PERSPECTIVE  DRAWING, 


the  direction  bav  He  now  sees  the  top  of  No.  2,  but  the  top  of 
No.  1 seems  some  distance  above,  and  he  naturally  concludes  that 
No.  2 appears  shorter  than  No.  1.  As  the  observer  looks  at  the 
top  of  No.  2,  No.  3 is  still  invisible,  and,  in  order  to  see  it,  he  has 
to  lower  his  eye  still  farther.  Comparing  the  bottoms  of  the  posts, 
he  finds  the  same  apparent  diminution  in  size  as  the  distance  of 
the  posts  from  his  eye  increases.  The  length  of  the  second  post 
appears  only  equal  to  the  distance  mn  as  measured  on  the  first 
post,  while  the  length  of  the  third  post  appears  only  equal  to  the 
distance  os  as  measured  on  post  No.  1. 

11.  In  the  same  way  that  the  lamp-posts  appear  to  diminish 
in  size  as  they  recede  from  the  eye,  the  parallel  lines  («,  aY, 
a2,  etc.,  and  c,  cv  <?2,  etc.)  which  run  along  the  tops  and  bot- 
toms of  the  posts  appear  to  converge  as  they  recede,  for  the  dis- 
tance between  these  lines  seems  less  and  less  as  it  is  taken  farther 
and  farther  away.  At  infinity  the  distance  between  the  lines  be- 
comes zero,  and  the  lines  appear  to  meet  in  a single  point.  This 
point  is  called  the  vanishing  point  of  the  lines. 

12.  If  any  object,  as,  for  illustration,  a cube,  is  studied,  it 
will  be  seen  that  the  lines  which  form  its  edges  may  be  separated 


tern.  For  example,  in  Fig.  4,  A,  AI?  A2,  and  Ag  belong  to  one 
group  or  system  ; B,  B1?  B2,  and  B3,  to  another ; and  C,  Cx,  C2,  and 
C8,  to  a third.  Each  system  has  its  own  vanishing  point,  towards 
which  all  the  elements  of  that  system  appear  to  converge.  This 
phenomenon  is  well  illustrated  in  the  parallel  lines  of  a railroad 
track,  or  by  the  horizontal  lines  which  form  the  courses  of  a stone 
wall. 


into  groups  according 
to  their  different  direc- 
tions ; all  lines  having 
the  same  direction  form- 
ing one  group,  and  ap- 
parently converging  to 
a common  vanishing 
point.  Each  group  of 
parallel  lines  is  called  a 
system,  and  each  line 
an  element  of  the  sys- 


252 


PERSPECTIVE  DRAWING. 


13.  As  all  lines  which  belong  to  the  same  system  appear  to 
meet  at  the  vanishing  point  of  their  system,  it  follows  that  if  the 
eye  is  placed  so  as  to  look  directly  along  any  line  of  a system , that 
line  will  be  seen  endwise , and  appear  as  a point  exactly  covering  the 
vanishing  point  of  the  system  to  which  it  belongs. 

If,  for  illustration,  the  eye  glances  directly  along  one  of  the 
horizontal  lines  formed  by  the  courses  of  a stone  wall,  this  line 
will  be  seen  as  a point,  and  all  the  other  horizontal  lines  in  the 
wall  will  apparently  converge  towards  the  point.  In  other  words, 
the  line  along  which  the  eye  is  looking  appears  to  cover  the  van- 
ishing point  of  the  system  to  which  it  belongs.  Thus,  the  vanish- 


ing point  of  any  system  of  lines  must  lie  on  that  element  of  the 
system  which  enters  the  observer’s  eye,  and  must  be  at  an  infinite 
distance  from  the  observer.  Therefore,  to  find  the  vanishing 
point  of  any  system  of  lines,  imagine  one  of  its  elements  to  enter 
the  observer’s  eye.  This  element  is  called  the  visual  element  of 
the  system,  and  may  often  be  a purely  imaginary  line  indicating 
simply  the  direction  in  which  the  vanishing  point  lies.  The  van- 
ishing point  will  always  be  found  on  this  visual  element  and  at  an 
infinite  distance  from  the  observer. 

14.  To  further  illustrate  this  point,  suppose  an  observer  to 
be  viewing  the  objects  in  space  represented  in  Fig.  5.  lie  desires 


253 


PERSPECTIVE  DRAWING. 


o 


to  find  the  vanishing  point  for  the  system  of  lines  parallel  to  the 
oblique  line  ab  which  forms  one  edge  of  the  roof  plane  abed. 
There  are  two  lines  in  the  roof  that  belong  to  this  system,  namely : 
ab  and  do  If  he  imagines  an  element  of  the  system  to  enter 
his  eye,  and  looks  directly  along  this  element,  he  will  be  look- 
ing in  a direction  exactly  parallel  to  the  line  ab , and  he  will 
be  looking  directly  at  the  vanishing  point  of  the  system  (§  13). 
This  visual  element  along  which  he  is  looking  is  a purely  imaginary 
line  parallel  to  ab  and  dc.  All  lines  in  the  object  belonging  to 
this  system  will  appear  to  converge  towards  a point  situated  on 
the  line  along  which  he  is  looking,  and  at  an  infinite  distance  from 
him. 

This  phenomenon  is  of  great  importance,  and  is  the  founda- 
tion of  most  of  the  operations  in  making  a perspective  drawing. 

15.  The  word  “ vanish  ” as  used  in  perspective  always  im- 
plies a recession.  Thus,  a line  that  vanishes  upward,  slopes  up- 
ward as  it  recedes  from  the  observer;  a line  that  vanishes  to  the 
right,  slopes  to  the  right  as  it  recedes  from  the  observer. 

16.  It  follows  from  paragraphs  13  and  14  that  any  system 
of  lines  that  vanishes  upward,  will  have  its  vanishing  point  above 
the  observer’s  eye.  Similarly,  any  system  vanishing  downward, 
will  have  its  vanishing  point  below  the  observer’s  eye ; any  sys- 
tem vanishing  to  the  right,  will  have  its  vanishing  point  to  the 
right  of  the  observer’s  eye ; and  any  system  vanishing  to  the  left, 
will  have  its  vanishing  point  to  the  left  of  the  observer’s  eye. 
Any  system  of  horizontal  lines  will  have  its  vanishing  point  on  a 
level  with  the  observer’s  eye,  and  a system  of  vertical  lines  will 
have  its  vanishing  point  vertically  in  line  with  the  observer’s 
eye. 

17.  All  planes  that  are  parallel  to  one  another  are  said  to 
belong  to  the  same  system,  each  plane  being  called  an  element 
of  the  system. 

All  the  planes  of  one  system  appear  to  approach  one  another 
as  they  recede  from  the  eye,  and  to  meet  at  infinity  in  a single 
straight  line  called  the  vanishing  trace  of  the  system.  Thus, 
the  upper  and  lower  faces  of  a cube  seen  in  space,  will  appear  to 
converge  toward  a straight  line  at  infinity. 

18.  If  the  eye  is  so  placed  as  to  look  directly  along  one  of 


254 


PERSPECTIVE  DRAWING. 


the  planes  of  a system,  that  plane  will  be  seen  edgewise,  and  will 
appear  as  a single  straight  line  exactly  covering  the  vanishing 
trace  of  the  system  to  which  it  belongs.  The  plane  of  any  system 
that  passes  through  the  observer’s  eye  is  called  the  visual  plane 
of  that  system. 

19.  From  § 18,  it  follows  that  the  vanishing  trace  of  a system 
of  planes  that  vanishes  upward,  will  be  found  above  the  level  of  the 
eye,  while  the  vanishing  trace  of  a system  of  planes  vanishing 
downward,  will  be  found  below  the  level  of  the  eye.  The  vanish- 
ing trace  of  a system  of  vertical  planes  will  be  a vertical  line  ; and 
of  a system  of  horizontal  planes,  a horizontal  line,  exactly  on  a 
level  with  the  observer’s  eye. 

20.  The  vanishing  trace  of  the  system  of  horizontal  planes 
is  called  the  horizon. 

The  visual  plane  of  the  horizontal  system  is  called  the  plane 
of  the  horizon.  The  plane  of  the  horizon  is  a most  important  one 
in  the  construction  of  a perspective  projection. 

21.  From  the  foregoing  discussion  the  truth  of  the  following 
statements  will  be  evident.  They  may  be  called  the  Five  Axioms 
of  Perspective. 

(ci)  All  the  lines  of  one  system  appear  to  converge  and  to 
meet  at  an  infinite  distance  from  the  observer's  eye , in  a single 
point  called  the  vanishing  point  of  the  system. 

(5)  All  the  planes  of  one  system  appear  to  converge  as  they 
recede  from  the  eye,  and  to  meet  at  an  infinite  distance  from  the 
observer , in  a single  straight  line  called  the  vanishing  trace  of  the 
system. 

(c)  Any  line  lying  in  a plane  will  have  its  vanishing  point 
somewhere  in  the  vanishing  trace  of  the  plane  in  which  it  lies. 

fiV)  The  vanishing  trace  of  any  plane  must  pass  through  the 
vanishing  points  of  all  lines  that  lie  in  it.  Thus , since  the  van- 

ishing trace  of  a plane  is  a straight  line  (§  18),  the  vanishing  points 
of  any  two  lines  lying  in  a plane  ivill  determine  the  vanishing  trace 
of  the  system  to  which  the  p>lane  belongs. 

Qe')  As  the  intersection  of  two  planes  is  a line  lying  in  both , 
the  vanishing  point  of  this  intersection  must  lie  in  the  vanishing 
traces  of  both  planes,  and  hence,  at  the  point  where  the  vanishing 
traces  of  the  two  planes  cross.  In  other  words,  the  vanishing  point 


10 


PERSPECTIVE  DRAWING. 


of  the  intersection  of  two  planes  must  lie  at  the  intersection  of  the 
vanishing  traces  of  the  two  planes. 

22.  The  five  axioms  in  the  last  paragraph  are  the  statements 
of  purely  imaginary  conditions  which  appear  to  exist,  but  in 
reality  do  not.  Thus,  parallel  lines  appear  to  converge  and  to 
meet  at  a point  at  infinity,  but  in  reality  they  are  exactly  the 
same  distance  apart  throughout  their  length.  Parallel  planes 
appear  to  converge  as  they  recede,  but  this  is  a purely  apparent 
condition,  and  not  a reality ; the  real  distance  between  the  planes 
does  not  change. 

23.  The  perspective  projection  represents  by  real  conditions 
the  purely  imaginary  conditions  that  appear  to  exist  in  space. 


Thus,  the  apparent  convergence  of  lines  in  space  is  represented 
by  a real  convergence  in  the  perspective  projection.  Again,  the 
vanishing  point  of  a system  of  lines  is  a purely  imaginary  point 
which  does  not  exist.  But  this  imaginary  point  is  represented  in 
perspective  projection  by  a real  point  on  the  picture  plane. 

From  § 14,  the  vanishing  point  of  any  system  of  lines  lies 
upon  the  visual  element  of  that  system.  This  visual  element 
may  be  considered  to  be  the  visual  ray  which  projects  the  vanish- 


256 


PERSPECTIVE  DRAWING. 


11 


mg  point  to  the  observer’s  e}^e.  Hence,  from  § T,  the  intersection  of 
this  visual  element  with  the  picture  plane  will  be  the  perspective 
of  the  vanishing  point  of  the  system  to  which  it  belongs.  This 
is  illustrated  in  Fig.  6.  The  object  in  space  is  shown  on  the 
right  of  the  figure.  If  the  observer  wishes  to  find  the  vanishing 
point  of  the  oblique  line  ab  in  the  object  in  space,  he  imagines  a 
line  parallel  to  ab  to  enter  his  eye,  and  looks  along  this  line  (§  13). 
Where  this  line  along  which  he  is  looking  pierces  the  picture 
plane,  will  be  the  perspective  of  the  vanishing  point.  Further- 
more, the  perspective  of  the  line  ab  has  been  found  by  drawing 
the  visual  rays  from  a and  b respectively,  and  finding  where  these 
rays  pierce  the  picture  plane  (§  7).  These  points  are  respectively, 
aF  and  bp,  and  the  straight  line  drawn  between  a?  and  bv  is  the 
perspective  of  the  line  ab.  The  perspective  of  the  line  albl  which 
is  parallel  to  ab , has  been  found  in  a similar  way,  and  it  will  be 
noticed  that  its  perspective  projection  ( a\  6f)  actually  converges 
towards  avbv  in  such  a manner  that  if  these  two  lines  are  pro- 
duced they  will  actually  meet  at  the  perspective  of  the  vanish- 
ing point  of  their  system. 

Note. — It  is  evident  that  the  perspective  of  a straight  line  will 
always  be  a straight  line , the  extreme  points  of  which  are  the  perspec- 
tives of  the  extremities  of  the  given  line. 

24.  Thus,  the  five  axioms  of  perspective  may  be  applied 
to  Perspective  Projection  as  follows  : — 

(ci)  Parallel  lines  do  converge  and  meet  at  the  vanishing 
point  of  their  system. 

(b)  Parallel  planes  do  converge  and  meet  at  the  vanishing 
trace  of  their  system. 

(c)  The  vanishing  point  of  any  line  lying  in  a plane  will  be 
found  in  the  vanishing  trace  of  the  plane. 

Therefore , the  vanishing  points  of  all  horizontal  lines  will  be 
found  in  the  horizon  (§  20). 

( d ) The  vanishing  trace  of  any  plane  will  be  determined  by 
the  vanishing  points  of  any  two  lines  that  lie  in  it,  and  must  con- 
tain the  vanishing  points  of  all  lines  that  lie  in  it. 

( e ) The  vanishing  point  of  the  intersection  of  two  planes  will 
be  found  at  the  intersections  of  the  vanishing  traces  of  the  two  planes. 


257 


12 


PERSPECTIVE  DRAWING. 


To  the  five  axioms  of  perspective  projection  already  stated 
may  be  added  the  following  three  truths  concerning  the  construc- 
tion of  the  perspective  projection  : — • 

(/)  The  perspective  of  any  point  in  space  is  where  the 
visual  ray  through  the  point  pierces  that  picture  plane  (§7). 

(g)  The  perspective  of  the  vanishing  point  of  any  system  of 
lines  is  where  the  visual  element  of  that  system  pierces  the  j)ic- 
ture  plane. 

Rule  for  fi7iding  the  perspective  of  the  vanishing  point  of  any 
system  of  lines : — Draw  an  element  of  the  system  through  the  ob- 
server’s eye , and  find  where  it  pierces  the  picture  plane. 

(h)  Any  point,  line,  or  surface  which  lies  in  the  picture 
plane  will  be  its  own  perspective,  and  show  in  its  true  size  and 
shape. 

25.  Knowing  how  to  find  the  perspective  of  any  point,  and 
how  to  find  the  vanishing  point  of  any  system  of  lines,  any  prob- 
lem in  perspective  may  be  solved.  Therefore,  it  may  be  said 
that  the  whole  process  of  making  a perspective  projection  reduces 
itself  to  the  problem  of  finding  where  a line  pierces  a plane. 

Before  proceeding  farther,  the  student  should  review  the 
first  twenty-five  paragraphs  by  answering  carefully  the  following 
questions  : — 

(1)  What  does  a perspective  projection  represent? 

(2)  What  is  a visual  ray? 

(3)  How  is  a perspective  projection  formed  ? 

(4)  How  does  a perspective  projection  differ  from  an  ortho 
graphic  projection  ? 

(5)  What  is  the  plane  called  on  which  the  perspective  pro 
jection  is  made  ? 

(6)  What  is  meant  by  the  term  Station  Point? 

(7)  What  is  the  most  important  phenomenon  of  perspective 

(8)  What  is  meant  by  a system  of  lines  ? 

(9)  What  is  meant  by  a system  of  planes  ? 

(10)  What  is  a visual  element? 

(11)  Define  vanishing  point. 

(12)  Define  vanishing  trace. 

(13)  Describe  the  position  of  the  vanishing  point  of  any  sy^ 
tem  of  lines. 


258 


PERSPECTIVE  DRAWING. 


13 


(14)  Give  the  five  axioms  of  perspective. 

(15)  Do  parallel  lines  in  space  really  converge? 

(16)  Do  the  perspective  projections  of  parallel  lines  really 
converge? 

(17)  Where  will  the  perspective  projections  of  parallel  lines 
meet? 

(18)  How  is  the  perspective  of  any  point  found? 

(19)  How  is  the  perspective  of  the  vanishing  point  of  any 
system  of  lines  found  ? 

(20)  What  will  be  the  perspective  of  a straight  line? 

(21)  What  is  meant  by  the  horizon  ? 

(22)  What  is  meant  by  the  plane  of  the  horizon  ? 

THE  PLANES  OF  PROJECTION. 

26.  Two  planes  of  projection  at  right  angles  to  one  another, 
one  vertical  and  the  other  horizontal,  are  used  in  making  a per- 
spective. In  Fig.  7 these  two  planes  are  shown  in  oblique  pro- 


jection. The  vertical  plane  is  the  picture  plane  (§  6 and  Fig.  7) 
on  which  the  perspective  projection  is  made,  and  corresponds 
exactly  to  the  vertical  plane,  or  vertical  coordinate  used  in  ortho- 
graphic projections. 


259 


14 


PERSPECTIVE  DRAWING. 


27.  The  horizontal  plane,  or  plane  of  the  horizon  (§  20  and 
Fig.  7),  always  passes  through  the  assumed  position  of  the  observer's 
eye , and  corresponds  exactly  to  the  horizontal  plane  or  horizontal 
coordinate  used  in  orthographic  projections. 

28.  All  points,  lines,  surfaces,  or  solids  in  space,  the  per- 
spective projections  of  which  are  to  be  found,  are  represented  by 
their  orthographic  projections  on  these  two  planes,  and  their  per- 
spectives are  determined  from  these  projections. 

29.  Besides  these  two  principal  planes  of  projection,  a third 
plane  is  used  to  represent  the  plane  on  which  the  object  is  sup- 
posed to  rest  (Fig.  7).  This  third  plane  is  horizontal,  and  is 
called  the  plane  of  the  ground.  Its  relation  to  the  plane  of  the 
horizon  determines  the  nature  of  the  perspective  projection.  To 
illustrate  : The  observer’s  eye  must  always  be  in  the  plane  of  the 
horizon  (§  27),  while  the  object,  the  perspective  of  which  is  to  be 
made,  is  usually  supposed  to  rest  upon  the  plane  of  the  ground. 
In  most  cases  the  plane  of  the  ground  will  also  be  the  plane  on 
which  the  observer  is  supposed  to  stand,  but  this  will  not  always 
be  true.  The  observer  may  be  standing  at  a much  higher  level 
than  the  plane  on  which  the  object  rests,  or  he  may  be  standing 
below  that  plane.  It  is  evident,  therefore,  that  if  the  plane  of 
the  ground  is  chosen  far  below  the  plane  of  the  horizon,  the 
observer’s  eye  will  be  far  above  the  object,  and  the  resulting  per- 
spective projection  will  be  a “ bird’s-eye  view.”  If,  on  the  other 
hand,  the  plane  of  the  ground  is  chosen  above  the  plane  of  the 
horizon,  the  observer’s  eye  will  be  below  the  object,  and  the  re- 
sulting perspective  projection  will  show  the  object  as  though 
being  viewed  from  below.  This  has  sometimes  been  called  a 
“ worm’s-eye  view,”  or  a “ toad’s-eye  view.” 

Usually  the  plane  of  the  ground  is  chosen  so  that  the  dis- 
tance between  it  and  the  plane  of  the  horizon  is  about  equal  (at 
the  scale  of  the  drawing)  to  the  height  of  a man.  This  is  the  posi- 
tion indicated  in  Fig.  7,  and  the  resulting  perspective  will  show 
the  object  as  though  seen  by  a man  standing  on  the  plane  on 
which  the  object  rests. 

80.  The  intersection  of  the  picture  plane  and  the  plane  of  the 
horizon  corresponds  to  the  ground  line  used  in  the  study  of  pro- 
jections, in  Mechanical  Drawing.  For  more  advanced  work,  how- 


260 


PERSPECTIVE  DRAWING. 


15 


ever,  there  is  some  objection  to  this  term.  The  intersection  of 
the  two  coordinate  planes  has  really  no  connection  with  the 
ground,  and  if  the  term  “ ground  line  ” is  used,  it  is  apt  to  result 
in  a confusion  between  the  intersection  of  the  two  coordinate 
planes,  and  the  intersection  of  the  auxiliary  plane  of  the  ground, 
with  the  picture  plane. 

31.  The  intersection  of  the  two  coordinate  planes  is  usually 
lettered  VH  on  the  picture  plane,  and  HPP  on  the  plane  of  the 
horizon.  (See  Fig.  7.)  That  is  to  say : When  the  vertical  plane 
is  being  considered,  VH  represents  the  intersection  of  that  plane 
with  the  plane  of  the  horizon.  It  should  also  be  considered  as 
the  vertical  projection  of  the  plane  of  the  horizon.  See  Mechani- 
cal* Drawing  Part  III,  page  5,  paragraph  in  italics.  All  points, 
lines,  or  surfaces  lying  in  the  plane  of  the  horizon  will  have  their 
vertical  projection  in  VH. 

32.  On  the  other  hand,  when  the  horizontal  plane  is  being 
considered,  HPP  represents  the  intersection  of  the  two  planes, 
and  also  the  horizontal  projection  of  the  picture  plane.  All  points, 
lines,  or  surfaces  in  the  picture  plane  will  have  their  horizontal 
projections  in  HPP.  Thus,  instead  of  considering  the  inter- 
section of  the  two  coordinate  planes  a single  line,  it  should  be 
considered  the  coincidence  of  two  lines,  i.e. : First,  the  vertical 
projection  of  the  plane  of  the  horizon ; second,  the  horizontal 
projection  of  the  picture  plane. 

33.  The  plane  of  the  ground  is  always  represented  by 
its  intersection  with  the  picture . plane  (see  VHt  Fig.  7).  Its 
only  use  is  to  determine  the  relation  between  the  plane  of 
the  horizon  and  the  plane  on  which  the  object  rests  (§  29). 
The  true  distance  between  these  two  planes  is  always  shown 
by  the  distance  between  VH  and  VHX  as  drawn  on  the  picture 
plane. 

34.  To  find  the  perspective  of  a point  determined  by  its 
vertical  and  horizontal  projections. 

Fig.  8 is  an  oblique  projection  showing  the  two  coordinate 
planes  at  right  angles  to  each  other.  The  assumed  position  of 
the  plane  of  the  ground  is  indicated  by  its  vertical  trace 

(VH,). 


261 


16 


PERSPECTIVE  DRAWING. 


Note.  — The  vertical  trace  of  any  plane  is  the  intersection  of 
that  plane  with  the  vertical  coordinate.  The  horizontal  trace  of 
any  plane  is  the  intersection  of  that  plane  with  the  horizontal 
coordinate. 

The  assumed  position  of  the  station  point  is  indicated  by  its 
two  projections,  SPV  and  SPH.  Since  the  station  point  lies  in 
the  plane  of  the  horizon  (§  27),  it  is  evident  that  its  true  position 
must  coincide  with  SPH,  and  that  (§  31)  its  vertical  projection 
must  be  found  in  VH,  as  indicated  in  the  figure.  Let  the  point  a 
represent  any  point  in  space.  The  perspective  of  the  point  a will 
be  at  ap,  where  a visual  ray  through  the  point  a pierces  the  pic- 
ture plane  (§  24).  We  may  find  av  in  the  following  manner,  by 
using  the  orthographic  projections  of  the  point  aT,  instead  of  the 
point  itself.  an  represents  the  horizontal  projection,  and  aY  repre- 
sents the  vertical  projection  of  the  point  a . A line  drawn  from 
the  vertical  projection  of  the  point  a to  the  vertical  projection  of 
the  station  point,  will  represent  the  vertical  projection  of  the  visual 
ray , which  passes  through  the  point  a.  In  Fig.  8 this  vertical 
projection  is  represented  by  the  line  drawn  on  the  picture  jfiane 
from  aY  to  SPV 

A line  drawn  from  the  horizontal  projection  of  a to  the  hori- 
zontal projection  of  the  station  point  will  represent  the  horizontal 
projection  of  the  visual  ray , which  passes  through  the  point  a.  In 
Fig.  8,  this  horizontal  projection  is  represented  by  the  line  drawn 
on  the  plane  of  the  horizon  from  aH  to  SPH.  Thus  we  have, 
drawn  upon  the  planes  of  projection,  the  vertical  and  horizontal 
projections  of  the  point  a , and  the  vertical  and  horizontal  projec- 
tions of  the  visual  ray  passing  between  the  point  a and  the  station 
point. 

35.  We  must  now  find  the  intersection  of  the  visual  ray 
with  the  picture  plane.  This  intersection  will  be  a point  in  the 
picture  plane.  It  is  evident  that  its  vertical  projection  must  coin- 
cide with  the  intersection  itself,  and  that  its  horizontal  projection 
must  be  in  HPP  (§  32).  But  this  intersection  must  also  be  on 
the  visual  ray  through  the  point  a,  and  consequently  the  horizon- 
tal projection  of  this  intersection  must  be  on  the  horizontal  pro- 
jection of  the  visual  ray.  Therefore,  the  horizontal  projection  of 
this  intersection  must  be  the  point  mn,  where  the  line  between 


k*/62 


Fi  g.  9a 


PERSPECTIVE  DRAWING. 


17 


SPH  and  aH  crosses  HPP.  The  vertical  projection  of  this  inter- 
section must  be  vertically  in  line  with  this  point,  and  on  the  line 
drawn  between  SPV  and  aY , and  hence  at  mv,  Since  the  vertical 
projection  of  the  intersection  coincides  with  the  intersection 
itself,  av  (coincident  with  rav)  must  be  the  perspective  of  the 
point  a . 

36.  This  is  the  method  of  finding  the  perspective  of  any 
point,  having  given  the  vertical  and  horizontal  projections  of 
the  point  and  of  the  station  point.  The  method  may  be  stated 
briefly  as  follows  : — 

Draw  through  the  horizontal  projection  of  the  point  and  the 
horizontal  projection  of  the  station  point,  a line  representing  the 
horizontal  projection  of  the  visual  ray,  which  passes  through 
the  point.  Through  the  intersection  of  this  line  with  HPP,  draw 
a vertical  line.  The  perspective  of  the  point  will  be  found  where 
this  vertical  line  crosses  the  vertical  projection  of  the  visual  ray, 
drawn  through  SPV  and  aY. 

37.  It  would  evidently  be  inconvenient  to  work  upon  two 
planes  at  right  angles  to  one  another,  as  shown  in  Fig.  8.  To 
avoid  this,  and  to  make  it  possible  to  work  upon  a plane  sur- 
face, the  picture  plane  (or  vertical  coordinate)  is  supposed  to 
be  revolved  about  its  intersection  with  the  plane  of  the  horizon, 
until  the  two  coincide  and  form  one  surface.  The  direction  of 
this  revolution  is  indicated  by  the  arrows  and  s2.  After  revo- 
lution, the  two  coordinate  planes  will  coincide,  and  the  vertical 
and  horizontal  projections  overlap  one  another,  as  indicated  in 
Fig.  9. 

It  will  be  noticed  that  the  coincidence  of  the  two  planes  in 
no  way  interferes  with  the  method  given  in  § 36,  of  finding  the 
perspective  (ap)  of  the  point  a,  from  the  vertical  and  horizontal 
projections  of  the  point.  Thus,  the  horizontal  projection  of  the 
visual  ray  through  the  point  will  be  seen,  drawn  from  SPH  to  aHf 
and  intersecting  HPP  in  the  point  mH.  The  vertical  projection 
of  the  visual  ray  through  the  point  will  be  seen  passing  from 
SPV  to  av.  And  av  is  found  upon  the  vertical  projection  of  the 
visual  ray,  directly  under  mK. 

It  will  readily  be  understood  that  in  a complicated  problem, 
the  overlapping  of  the  vertical  and  horizontal  projections  might 


265 


18 


PEESPECTIYE  DRAWING. 


result  in  some  confusion.  It  is,  therefore,  usually  customary, 
after  having  revolved  the  two  coordinate  planes  into  the  position 
shown  in  Fig.  9,  to  slide  them  apart  in  a direction  perpendicular 
to  their  line  of  intersection,  until  the  two  planes  occupy  a position 
similar  to  that  shown  in  Fig.  9a. 

38.  It  will  be  remembered  from  the  course  on  projections 
which  the  student  is  supposed  to  have  taken,  that  horizontal  pro- 
jections must  always  he  compared  with  horizontal,  and  never  with 
vertical  proj ections,  and  that  in  the  same  way,  vertical  projections 
must  always  he  compared  ivith  vertical,  and  never  with  horizontal 
projections.  It  is  evident  that  in  sliding  the  planes  apart,  the 
relations  between  the  projections  on  the  vertical  plane  will  not  be 
disturbed,  nor  will  the  relations  between  the  projections  on  the 
horizontal  plane,  and  consequently  it  will  make  no  difference 
how  far  apart  the  two  coordinate  planes  are  drawn,  provided  that 
horizontal  and  vertical  projections  of  the  same  points  are  always 
kept  in  line.  Thus,  in  Fig.  9a,  it  will  be  seen  that  in  drawing 
the  planes  apart,  aY  has  been  kept  in  line  with  an,  mY  with  mK, 
SPV  with  SPH,  etc. 

39.  It  will  be  observed  that  in  sliding  the  planes  apart,  their 
line  of  intersection  has  been  separated  into  its  two  projections 
(§§  31  and  32).  II PP,  being  on  the  plane  of  the  horizon  or  hori- 
zontal coordinate,  is  the  horizontal  projection  of  the  intersection  of 
the  two  planes,  while  VII,  being  on  the  picture  plane  or  vertical 
coordinate,  is  the  vertical  projection  of  the  intersection  of  the  two 
planes.  In  the  original  position  of  the  planes  (Fig.  9)  these 
two  projections  were  coincident.  The  distance  between  II PP 
and  VH  always  represents  the  distance  through  which  the  planes 
have  been  slid.  This  distance  is  immaterial,  and  will  have  no 
effect  on  the  perspective  drawing.  VHj  represents  the  vertical 
trace  of  the  plane  of  the  ground. 

In  this  figure,  as  in  the  case  of  Fig.  9,  the  student  should 
follow  through  the  construction  of  the  perspective  of  the  point  a, 
applying  the  method  of  § 36. 

40.  Fig.  10  shows  the  position  of  the  two  coordinate  planes 
and  of  the  plane  of  the  ground,  as  they  are  usually  represented 
on  the  drawing  board  in  making  a perspective  drawing.  It  is 
essentially  the  same  thing  as  Fig.  9a,  except  that  the  ]atter  was 


266 


PERSPECTI V E DR AWI N( i . 


shown  in  oblique  projection  in  order  that  its  development  from 
the  original  position  of  the  planes  (Fig.  8)  might  he  followed 
more  readily.  The  two  coordinate  planes  are  supposed  to  lie  in 
the  plane  of  the  paper. 

HPP  represents  the  horizontal  projection  of  the  picture 
plane,  and  YI1  represents  the  vertical  projection  of  the  plane  of 
the  horizon. 

As  horizontal  projections  are  never  compared  with  vertical 
projections  (§  38),  HPP  may  he  drawn  as  far  from,  or  as  near, 
YII  as  desired,  without  in  any 
way  affecting  the  resulting  per- 
spective drawing.  HPP  and  YH 
were  coincident  in  Fig.  9,  and  the 
distance  between  them  in  Fief.  10 
simply  shows  the  distance  that  the 
two  planes  have  been  slid  apart,  as 
illustrated  in  Fig.  9a.  As  already 
stated,  this  distance  is  immaterial, 
and  may  be  made  whatever  is  most 
convenient,  according  to  the  nature 
of  the  problem. 

If  HPP  should  be  placed 
nearer  the  top  of  the  sheet,  an  and 
SPH,  both  being  horizontal  projec- 
tions, would  follow  it,  the  relation 
between  these  horizontal  projec- 
tions always  being  preserved. 

On  the  other  hand,  SPV,  av,  a}\  YII,  and  YH1?  all  being  pro- 
jections on  the  vertical  plane,  must  preserve  their  relation  with 
one  another,  and  will  in  no  way  be  affected  if  the  group  of 
projections  on  the  horizontal  coordinate  is  moved  nearer  or 
farther  away.  It  must  be  borne  in  mind,  however,  that,  in  all 
cases,  the  vertical  and  horizontal  projections  of  corresponding 
points  must  be  kept  vertically  in  line.  Thus,  aH  must  always  be 
vertically  in  line  with  aY.  The  vertical  distance  between  these 
two  projections  does  not  matter,  provided  the  distance  from 
aK  to  HPP,  or  the  distance  from  aY  to  YII,  is  not  changed.  This 
point  cannot  be  too  strongly  emphasized. 


267 


20 


PERSPECTIVE  DRAWING. 


41.  Suppose  it  is  desired  to  determine  from  Fig.  10  how 
far  the  station  point  lies  in  front  of  the  picture  plane.  This  is  a 
horizontal  distance,  and  therefore  will  he  shown  by  the  distance 
between  the  horizontal  projection  of  the  station  point  and  the 
horizontal  projection  of  the  picture  plane,  or,  in  other  words,  by 
the  distance  between  SPH  and  HPP. 

42.  The  point  a is  a certain  distance  above  or  below  the 
plane  of  the  horizon.  This  is  a vertical  distance , and  will  be 
shown  by  the  distance  between  the  vertical  projection  of  the  point 
a and  the  vertical  projection  of  the  plane  of  the  horizon;  in  other 
words,  by  the  distance  between  aY  and  YH.  It  will  be  seen  that 
in  Fig.  10  the  point  a lies  below  the  plane  of  the  horizon. 

43.  If  it  be  desired  to  find  how  far  in  front  or  behind  the 
picture  plane  the  point  a lies,  this  is  a horizontal  distance , and 
will  be  shown  by  the  distance  between  the  horizontal  projection  of 
the  picture  plane  and  horizontal  projection  of  the  point  a , that  is, 
by  the  distance  between  HPP  and  a11.  In  Fig.  10  the  point  a 
lies  behind  the  picture  plane. 

44.  The  distance  between  the  plane  of  the  ground  and  the 
plane  of  the  horizon  is  a vertical  distance,  and  will  be  shown  by 
the  distance  between  the  vertical  projection  of  the  plane  of  the 
horizon  and  the  vertical  projection  of  the  plane  of  the  ground  ; i.e., 
the  distance  between  YH  and  YHX.  The  distance  between  the 
observer’s  eye  and  the  jfiane  0f  the  ground  is  also  a vertical  dis- 
tance, and  will  be  shown  by  the  distance  between  SPV  and  YHX; 
but  as  SPV  must  always  be  found  in  YH,  the  distance  of  the 
observer’s  eye  above  the  plane  of  the  ground  will  always  be  shown 
by  the  distance  between  VH  and  YHX. 

45.  To  find  the  perspective  of  the  point  a,  Fig.  10,  draw  the 
visual  ray  through  the  point,  and  find  where  this  visual  ray  pierces 
the  picture  plane  (§  24/).  The  horizontal  projection  of  the 
visual  ray  is  shown  by  the  line  RH  drawn  through  the  horizontal 
projection  SPH  of  the  observer’s  eye  and  the  horizontal  pro- 
jection aH  of  the  point  a.  The  vertical  projection  of  the  visual 
ray  is  shown  by  the  line  Rv  drawn  through  the  vertical  projec- 
tion SPV  of  the  observer’s  eye  and  the  vertical  projection  aY 
of  the  point  a.  This  visual  ray  pierces  the  picture  plane  at 
the  point  ap  on  Rv  vertically  in  line  with  the  point  where 


268 


PERSPECTIVE  DRAWING. 


21 


RH  crosses  HPP  (§§  35  and  36).  av  is  the  perspective  of  the 
point  a. 

Note.  — To  find  where  any  line,  represented  by  its  horizon- 
tal and  vertical  projections,  pierces  the  picture  plane,  is  one  of 
the  most  used  and  most  important  problems  in  perspective  projec- 
tion. The  point  where  any  line  pierces  the  picture  plane  will 
always  be  found  on  the  vertical  projection  of  the  line,  vertically 
above  or  below  the  point  where  the  horizontal  projection  of  the 
line  crosses  HPP  (§§  35  and  36). 


NOTATION. 

46.  In  order  to  avoid  confusion  between  the  vertical,  hori- 
zontal, and  perspective  projections  of  the  points  and  lines  in  the 
drawing,  it  becomes  necessary  to  adopt  some  systematic  method 
of  lettering  the  different  points  and  lines.  The  following  method 
will  be  found  convenient,  and  has  been  adopted  in  these  notes. 

If  the  student  will  letter  each  point  or  line  as  it  is  found,  in 
accordance  with  this  notation,  he  will  be  able  to  read  his  drawings 
at  a glance,  and  any  desired  projection  of  a point  or  line  may  be 
recognized  instantly. 

The  picture  plane  (or  vertical  coordinate)  is  indicated  by 
the  capital  letters  PP. 

The  plane  of  the  horizon  (or  horizontal  coordinate)  is  indi- 
cated by  the  capital  letter  H. 

A point  in  space  is  indicated  by  a small  letter. 

The  same  small  letter  with  an  index  v,  H,  or  p,  indicates  its 
vertical , horizontal , or  perspective  projection,  respectively. 

A line  in  space  is  indicated  by  a capital  letter,  usually  one  of 
the  first  letters  in  the  alphabet. 

The  same  capital  letter  with  an  index  v,  H,  or  r,  indicates  its 
vertical , horizontal , or  perspective  projection,  respectively. 

All  lines  which  belong  to  the  same  system  may  be  designated 
by  the  same  letter,  the  different  lines  being  distinguished  by  the 
subordinate  v 2,  3,  etc.,  placed  after  the  letter. 

The  trace  of  a plane  upon  the  picture  plane  is  indicated  by  a 
capital  letter  (usually  one  of  the  last  letters  in  the  alphabet)  with 
a capital  V placed  before  it. 


269 


22 


PERSPECTIVE  DRAWING. 


The  same  letter  preceded  by  a capital  IT  indicates  the  trace 
of  the  plane  upon  the  horizontal  coordinate. 

The  perspective  of  the  vanishing  trace  of  a system  of  planes  is 
indicated  by  a capital  letter  preceded  by  a capital  T. 

The  perspective  of  the  vanishing  point  of  a system  of  lines  is 
indicated  by  a small  v with  an  index  corresponding  to  the  letter 
of  the  lines  which  belong  to  the  system. 

PP  = vertical  coordinate,  or  picture  plane. 

HPP  = horizontal  trace  of  the  vertical  coordinate,  or  picture 
plane. 

H = horizontal  coordinate,  or  plane  of  the  horizon. 

VH  =s  vertical  trace  of  the  horizontal  coordinate,  or  plane  of 
the  horizon. 

H1  = plane  of  the  ground. 

VH1  = vertical  trace  of  the  plane  of  the  ground. 

a = point  in  space. 

aY  = vertical  projection  of  the  point. 

qHS  horizontal  projection  of  the  point. 

a?  = perspective  projection  of  the  point. 

A = line  in  space. 

Av  = vertical  projection  of  the  line. 

Ap  = perspective  projection  of  the  line. 

VS  = trace  of  the  plane  S upon  PP  (vertical  trace). 

ITS  = trace  of  the  plane  S upon  H (horizontal  trace). 

TS  = perspective  of  the  vanishing  trace  of  the  plane  S.  (See 
Note  I below.) 

vA  = perspective  of  the  vanishing  point  of  a system  of  lines, 
the  elements  of  which  are  lettered  A1?  A2,  A3,  A4,  etc.  (See  Note 
2 below.) 

Note  1.  — A plane  in  space  may  also  be  designated  by  the 
letters  of  any  two  lines  which  lie  in  it.  Thus,  the  plane  AH 
would  be  a plane  determined  by  the  two  lines  A and  B.  TAB 
would  indicate  the  perspective  of  the  vanishing  trace  of  the  plane. 

Note  2.  — A straight  line  may  be  designated  by  the  letters 
of  any  two  points  which  lie  in  it.  Thus,  the  line  ab  would  be  a 
straight  line  determined  by  the  two  points  a and  b.  vab  would  indi- 
cate the  perspective  of  the  vanishing  point  of  the  line.  It  is  some- 
times convenient  to  use  this  notation  in  place  of  the  general  one. 


270 


PERSPECTIVE  DRAWING. 


ELEMENTARY  PROBLEMS. 

47.  PROBLEM  I.  Fig.  11.  To  find  the  perspective  of  a 
point.  The  point  to  be  situated  behind  the  picture  plane,  and 
above  the  plane  of  the  horizon.  The  observer’s  eye  to  be  in 
front  of  the  picture  plane. 

First  assume  HPP  and  VH  (§  40).  These  lines  may  be  drawn 
anywhere  on  the  paper,  HPP  usually  being  placed  some  distance 
above  VH,  in  order  to  avoid  confusion  between  horizontal  and 
vertical  projections.  The  position  of  the  point  with  respect  to  the 
coordinate  planes  must  now  be  established  by  means  of  its  verti- 
cal and  horizontal  projections.  aY  located  above  VH  will  rej>- 
resent  the  vertical  projection  of  the  point.  Its  horizontal 
projection  must  be  vertically  in  line  with  aY;  and  since  the  point 


is  to  be  behind  the  picture  plane,  its  horizontal  projection  must 
be  behind  the  horizontal  projection  of  the  picture  plane,  i.e., 
i"  behind  HPP.  Next  establish  the  position  of  the  observer’s  eye, 
or  station  point.  Its  vertical  projection  (SPV)  may  be  assumed 
anywhere  in  VH.  Its  horizontal  projection  (SPH)  must  be  verti- 
cally in  line  with  SPV  and  J"  in  front  of  HPP.  The  perspective 
of  the  point  a will  be  where  the  visual  ray  through  the  point 
pierces  the  picture  plane.  A line  RH  drawn  through  SPH  and 
&H  will  be  the  horizontal  projection  of  this  visual  ray.  Its  verti- 
cal projection  will  be  the  line  Rv  drawn  through  SPV  and  aY. 
The  perspective  av  of  the  point  will  be  found  on  Rv  vertically 
in  line  with  the  intersection  of  RH  and  HPP  (§  45,  note).  Com- 
pare with  the  construction  shown  in  Fig.  10  and  Fig  8. 


271 


24  PERSPECTIVE  DRAWING. 


48.  Figs.  12,  13,  and  14  illustrate  this  same  problem. 

In  Fig.  12,  the  point  a,  as  shown  by  its  vertical  and  horizon- 
tal projections,  is  situated  below  the  plane  of  the  horizon  and 
1"  behind  the  picture  plane.  av  is  the  perspective  of  the  point. 


HPP 


Fig.  13 


HFF 


Fig.  14 


In  Fig.  13,  the  point  a is  above  the  plane  of  the  horizon 
and  in  front  of  the  picture  plane,  a?  is  its  perspective. 

In  Fig.  14,  the  point  a is  below  the  plane  of  the  horizon 
and  4"  in  front  of  the  picture  plane.  ap  is  its  perspective. 

49.  PROBLEM  II.  Fig.  15.  To  find  the  perspective  of 
a line,  the  line  being  determined  by  its  vertical  and  horizontal 
projections. 

Let  HPP  and  VH  be  given  as  indicated  in  the  figure.  Let 
AH  represent  the  horizontal  projection  of  the  line,  its  two  ex- 
tremities being  represented  by  an  and  6H,  respectively.  Similarly, 

let  Av  be  the  vertical  projec- 
tion of  the  line,  aY  and  bY 
being  the  vertical  projections 
of  its  extremities.  Let  the 
position  of  the  observer’s  eye 
be  as  indicated  by  SPV  and 
SPH. 

The  perspective  of  the 
point  a has  been  found  by 
Problem  I.  at  a¥.  The  per- 
spective of  the  point  b has  been  found  by  Problem  I.  at  bT.  The 
line  (Ap),  joining  av  and  6P,  will  be  the  perspective  of  the  given 
line.  (See  note  under  § 23.) 


272 


PERSPECTIVE  DRAWING. 


50.  PROBLEM  III.  Fig.  16.  Having  given  the  vertical 
and  horizontal  projection  of  any  line,  to  find  the  perspective  of 
its  vanishing  point. 

Let  the  line  be  given  by  its  vertical  ancl  horizontal  projections 
(Av  and  AH),  as  indicated  in  the  figure.  SPV  and  SPH  represent 
the  position  of  the  observer’s  eye.  To  find  the  perspective  of  the 


vanishing  point  of  any  line,  draw  through  the  observer’s  eye  an 
element  of  the  system  to  which  the  line  belongs,  and  find  where  this 
element  pierces  the  picture  plane  (§  24  rf).  Through  SPH  draw 
AXH  parallel  to  AH,  and  through  SPV  draw  Axv  parallel  to  Av. 
AXH  and  Axv  represent  the  two  projections  of  a line  passing  through 
the  observer’s  eye  and  parallel  to  AHAV. 

This  line  pierces  the  picture  plane  at  vK , 
giving  the  perspective  of  the  required  vanish- 
ing point  (§  45,  note).  The  perspectives  of 
all  lines  parallel  to  AVAH  will  meet  at  vK. 

Figs.  17  and  18  illustrate  this  same 
problem. 

51.  In  Fig.  17,  the  line,  as  shown  by  its 
two  projections,  is  a horizontal  one  ; hence, 

A \ drawn  through  SPV  coincides  with  YH, 
and  the  vanishing  point  for  the  system  of  the  lines  must  be  found 
on  YH  at  as  indicated  (§  24  c ). 

Note.  — Systems  of  lines  which  vanish  upward  will  have 
their  vanishing  points  above  YH.  Systems  of  lines  which  vanish 
downward  will  have  their  vanishing  points  below  YH  (§  16). 


HPP 


Fig. 18 


SP" 


VH  AV!-VA 


< 


§ 


273 


26 


PERSPECTIVE  DRAWING. 


52.  In  Fig.  18,  the  given  line  is  perpendicular  to  the  picture 
plane ; hence,  Axv  must  be  a jioint  coincident  with  SPV ; and  as 
vK  will  always  he  found  on  Axv,  the  vanishing  point  of  the  line 
must  coincide  with  SPV 

Note. — In  a perspective  drawing,  the  vanishing  point  for 
a system  of  lines  perpendicular  to  the  picture  plane  will  always 
coincide  with  the  vertical  projection  of  the  observer’s  eye. 


METHOD  OF  THE  REVOLVED  PLAN. 

58.  PROBLEM  IV.  Fig.  19.  To  find  the  perspective  of 
a rectangular  block  resting  upon  a horizontal  plane  1"  below  the 
level  of  the  eye,  and  turned  so  that  the  long  side  of  the  block 
makes  an  angle  of  3o°  with  the  picture  plane. 

The  block  is  shown  in  plan  and  elevation  at  the  left  of  the 
figure.  The.  first  step  will  be  to  make  an  auxiliary  horizontal  pro- 
jection of  the  block  on  the  plane  of  the  horizon,  showing  the  exact 
position  of  the  block  as  it  is  to  be  seen  in  the  perspective  projec- 
tion. This  auxiliary  horizontal  projection  is  really  a revolved 
plan  of  the  object,  and  is  called  a Diagram.  It  is  the  general 
rule,  in  making  a perspective  projection,  to  place  the  object  behind 
the  picture  plane  with  one  of  its  principal  vertical  lines  lying  in 
the  picture  plane  (24  li ).  HPP  is  usually  drawn  near  the  upper 
edge  of  the  paper,  leaving  just  room  enough  behind  to  place  the 
auxiliary  plan  or  diagram.  In  the  figure  the  diagram  is  shown 
in  the  required  position,  i.e.,  with  one  of  its  long  sides  ( ccbfe ) 
making  an  angle  of  30°  with  the  picture  plane.  The  vertical  edge 
( ae ) of  the  block  is  supposed  to  lie  in  the  picture  plane.  VH 
may  now  be  drawn  parallel  to  HPP  at  any  convenient  distance 
from  it,  as  indicated.  YHL,  the  vertical  trace  of  the  plane  on 
which  the  block  is  supposed  to  rest,  should  be  assumed  in  accord- 
ance with  the  given  data,  i.e.,  1"  below  YH  (§  44). 

The  position  of  the  observer’s  eye  should  next  be  established. 
SPH  is  its  horizontal  projection,  and  shows  by  its  distance  from 
HPP  the  distance  in  front  of  the  picture  plane  at  which  the  ob- 
server is  supposed  to  stand.  SPV  is  its  vertical  projection,  and  must 
always  be  found  in  YH.  In  this  problem  the  station  point  is  1 
in  front  of  the  picture  plane. 


274 


PERSPECTIVE  DRAWING. 


Note.  — As  a general  rule,  it  is  well  to  assume  the  station 
point  on  a vertical  line  half  way  between  two  lines  dropped  from 
the  extreme  edges  of  the  diagram,  as  indicated.  This  is  not 
necessary,  but,  as  will  be  explained  later,.  it  usually  insures  a 
more  pleasing  perspective  projection. 

Next  find  the  vanishing  points  for  the  different  systems  of 
lines  in  the  object  (§  12).  There  are  three  systems  of  lines  in  the 
block,  formed  by  its  three  sets  of  parallel  edges. 

1st.  A system  formed  by  the  four  horizontal  edges  vanishing 
to  the  right : ab , ef,  dc , and  kg. 

2d.  A system  formed  by  the  four  horizontal  edges  vanishing 
towards  the  left:  ad,  ek , be,  and fg. 

3d.  A system  formed  by  the  four  vertical  edges. 

First  find  the  vanishing  point  for  the  system  parallel  to  ab 
by  drawing  through  the  station  point  a line  parallel  to  ab  and 
finding  where  it  pierces  the  picture  plane  (24  g).  A11  drawn 

through  SPir  is  the  horizontal  projection  of  such  a line.  Its  ver- 
tical projection  (Av),  drawn  through  SPV,  will  coincide  with  VII, 
and  its  vanishing  point  will  be  found  on  VH  at  vab  (§51).  All 
lines  in  the  perspective  of  the  object  that  are  parallel  to  ab  will 
meet  at  vah  (§  24  a).  In  a similar  manner  find  v&d,  which  will 
be  the  vanishing  point  for  all  lines  parallel  to  ad. 

54.  If  the  method  for  finding  any  vanishing  point  is  applied 
to  the  system  of  vertical  lines,  it  will  be  found  that  this  vanishing 
point  will  lie  vertically  over  SPV  at  infinity.  That  is  to  say, 
since  all  vertical  lines  are  parallel  to  the  picture  plane,  if  a ver- 
tical line  is  drawn  through  the  station  point,  it  will  never  pierce 
the  picture  plane.  Therefore  (24  g'),  the  perspective  of  the  van- 
ishing point  of  a vertical  line  cannot  be  found  within  any  finite 
limits,  but  will  be  vertically  over  SPV , and  at  an  infinite  distance 
from  it.  In  a perspective  projection  all  vertical  lines  are  drawn 
actually  vertical , and  not  converging  towards  one  another. 

Note.  — This  is  true  of  all  lines  in  an  object  which  are 
parallel  to  the  picture  plane.  Thus,  the  perspective  of  any  line 
which  is  parallel  to  the  picture  plane,  ivill  actually  be  parallel  to  the 
line  itself ; and  the  perspectives  of  the  elements  of  a system  of  lines 
parallel  to  the  picture  plane,  will  be  drawn  parallel  to,  and  not  con- 
verging towards , one  another.  That  this  must  be  so,  is  evident, 


28 


PERSPECTIVE  DRAWING. 


since,  if  the  perspectives  of  such  a system  of  lines  did  converge 
towards*  one  another,  they  would  meet  within  finite  limits.  But 
it  has  just  been  found  that  the  perspective  of  the  vanishing  point 
of  such  a system  is  at  infinity.  The  perspectives  of  the  elements 
of  any  system  can  meet  only  at  the  perspective  of  their  vanish- 
ing point,  and  must,  therefore,  in  a system  parallel  to  the  picture 
plane,  be  drawn  parallel  to  one  another. 

The  directions  of  the  perspectives  of  all  lines  in  the  object 
have  now  been  determined,  and  will  be  as  follows : 

All  lines  parallel  to  ah  will  meet  at  vab. 

All  lines  parallel  to  ad  will  meet  at  v*a. 

All  vertical  lines  will  be  drawn  vertical. 

Since  the  point  e is  in  the  base  of  the  object,  it  lies  on  the 
plane  of  the  ground,  and  also,  since  the  line  ae  lies  in  the  picture 
plane,  the  point  e must  lie  on  the  intersection  of  the  plane  of  the 
ground  with  the  picture  plane.  Therefore,  the  point  e must  lie 
in  VH  , and  must  be  vertically  under  the  point  e in  the  diagram. 
Since  the  point  e lies  in  the  picture  plane,  it  will  be  its  own  per- 
spective ; and  ev  will  be  found  on  VI/,  vertically  under  e in  the 
diagram,  as  shown  in  the  figure.  From  ev  the  perspective  of  the 
lower  edges  of  the  cube  will  vanish  at  vAh  and  vad,  respectively, 
as  indicated. 

/p  is  the  perspective  of  the  point/,  and  will  be  found  on  the 
lower  edge  of  the  block,  vertically  under  the  intersection  of  HPP 
with  the  horizontal  projection  of  the  visual  ray  drawn  through  the 
point  / in  the  diagram. 

Similarly,  Jcv  is  found  on  the  lower  edge  of  the  block,  verti- 
cally under  the  intersection  of  HPP  and  the  visual  ray  drawn 
through  the  point  k in  the  diagram. 

Vertical  lines  drawn  through /p,  ev , and  &p,  will  represent  the 
perspectives  of  the  visible  vertical  edges  of  the  block. 

The  edge  evav  being  in  the  picture  plane  will  be  its  own  per- 
spective, and  show  in  its  true  size  (§24  A).  Therefore,  av  may  be 
established  by  making  the  distance  evav  equal  to  eYav  as  taken 
from  the  given  elevation.  From  aF  two  of  the  upper  horizontal 
edges  of  the  block  will  vanish  at  vah  and  vad,  respectively,  estab- 
lishing the  points  hv  and  c2p,  by  their  intersections  with  the  vertical 
edges  drawn  through  kv  and /p,  respectively.  Lines  drawn  through 


278 


PERSPECTIVE  DRAW  I XG. 


20 


<F  and.  bp,  and  yanishing  respectively  at  vilh  and  v**1,  will  intersect 
at  c p,  and  complete  the  perspective  of  the  block. 

Before  going  farther  in  the  notes,  the  student  should  solve 
the  problems  on  Plate  I. 

LINES  OF  AAEASURES. 

55.  Any  line  which  lies  in  the  picture  plane  will  be  its  own 
perspective,  and  show  the  true  length  of  the  line  (24  li).  Such 
a line  is  called  a Line  of  Measures. 

In  the  last  problem,  the  line  ae,  being  in  the  picture  plane, 
was  a line  of  measures  ; that  is  to  say,  its  length  could  be  laid  off 
directly  from  the  given  data,  and  from  this  length  the  lengths  of 
the  remaining  lines  in  the  perspective  drawing  could  be  established. 
Fig.  20  shows  a similar  problem.  The  line  ae  lies  in  the  picture 
plane,  and  ave p is,  therefore,  a line  of  measures  for  the  object. 

56.  Besides  this  principal  line  of  measures,  other  lines  of 
measures  may  easily  be  established  by  extending  any  vertical  plane 
in  the  object  until  it  intersects  the  picture  plane.  This  intersec- 
tion, since  it  lies  in  the  picture  plane,  will  show  in  its  true  size, 
and  will  be  an  auxiliary  line  of  measures.  All  points  in  it  will 
show  at  their  true  height  above  the  plane  of  the  ground.  Thus, 
in  Fig.  20,  avev  is  the  principal  line  of  measures,  and  shows  the 
true  height  of  the  block.  If  the  rear  vertical  faces  of  the  block 
are  extended  till  they  intersect  the  picture  plane,  these  intersec- 
tions (mpnp  and  oppp)  will  be  auxiliary  lines  of  measures,  and  will 
also  show  the  true  height  of  the  block.  It  will  be  noticed  in  the 
figure  that  mTw?  and  ovpv  are  each  equal  to  aveT.  Either  one  of 
these  lines  could  have  been  used  to  determine  the  vertical  height 
of  the  perspective  of  the  block.  For  illustration,  suppose  it  is  de- 
sired to  find  the  height  of  the  perspective,  using  the  line  ovpv  as 
the  line  of  measures.  Assume  the  vanishing  points  (rad  and  vab) 
for  the  two  systems  of  horizontal  edges  in  the  block  to  have  been 
established  as  in  the  previous  case.  Now  extend  the  line  he  (in 
the  diagram),  which  represents  the  horizontal  projection  of  the 
face  cbf,  till  it  intersects  HPP.  From  this  intersection  drop  a 
vertical  line  op  which  will  represent  the  intersection  of  the  vertical 
face  cbf  with  the  picture  plane,  and  will  be  a line  of  measures  for 
the  face.  pv,  where  this  line  of  measures  intersects  5 1 Ij,  will  be  the 


,30 


PERSPECTIVE  DRAWING. 


point  where  the  lower  horizontal  edge  (produced)  of  the  face  cbf 
intersects  the  picture  plane.  Measure  off  the  distance  y>pop  equal 
to  the  true  height  of  the  block,  as  given  by  the  elevation.  Two 
lines  drawn  through  op  and  pF  respectively,  and  vanishing  at  vad, 
will  represent  the  perspectives  of  the  upper  and  lower  edges  of  the 
face  cbf \ produced.  The  perspective  (6P),  of  the  point  b,  will  be 
found  on  the  perspective  of  the  upper  edge  of  the  face  cbf,  verti- 
cally below  the  intersection  of  HPP  with  the  horizontal  projection 
of  a visual  ray  drawn  through  the  point  b in  the  diagram.  A ver- 
tical line  through  bv  will  intersect  the  lower  horizontal  edge  of  the 
face  cbf  in  the  point /p.  Lines  drawn  respectively  through  bT  and 
/p,  vanishing  at  vab,  will  establish  the  perspectives  of  the  upper 
and  lower  horizontal  edges  of  the  face  abfe  The  points  aF  and 
eF  will  be  found  vertically  under  the  points  a and  e in  the  diagram. 
The  remainder  of  the  perspective  projection  may  now  easily  be 
determined. 

5T.  The  perspectives  of  any  points  on  the  faces  of  the  block 
may  be  found  by  means  of  the  diagram  and  one  of  the  lines  of 
measures. 

Let  the  points  gY , hY,  kY,  and  lY , in  the  given  elevation,  de- 
termine a square  on  the  face  abfe  of  the  block.  Let  the  points 
g,  h,  k,  and  l,  represent  the  position  of  the  square  in  the  diagram. 
Extend  the  upper  and  lower  horizontal  edges  of  the  square,  as 
shown  in  elevation,  until  they  intersect  the  vertical  edge  aYeY 
in  the  points  tY  and  vY . To  determine  the  perspective  of  the 
square,  lay  off  on  aFeF,  which  is  a line  of  measures  for  the  face 
abfe , the  divisions  tF  and  vF  taken  directly  from  the  elevation. 
Two  lines  drawn  through  tF  and  vF  respectively,  vanishing  at  vab, 
will  represent  the  perspectives  of  the  upper  and  lower  edges  (pro- 
duced) of  the  square.  gF  will  be  found  on  the  perspective  of  the 
upper  edge,  vertically  under  the  intersection  of  HPP  with  the 
horizontal  projection  of  a visual  ray  drawn  through  the  point  g in 
the  diagram.  The  position  of  kF  may  be  established  in  a similar 
manner.  Vertical  lines  drawn  through  gF  and  kF  respectively, 
will  complete  the  perspective  of  the  square. 

58.  The  auxiliary  line  of  measures  oFp?  might  have  been 
used  instead  of  aFeF.  In  this  case,  oFp>F  should  be  divided  by  the 
points  ivF  and  yF,  in  the  same  way  that  ae,  in  elevation,  is  divided 


280 


PERSPECT IYE  DR  A WING. 


31 


by  the  points  t and  v.  Through  wv  and  yv,  draw  horizontal  lines 
lying  in  the  plane  cbf,  for  which  cPpP  is  a line  of  measures.  These 
lines  will  vanish  at  vad,  and  intersect  the  vertical  edge  blfv  of  the 
block.  From  these  intersections  draw  horizontal  lines  lying  in 
the  plane  abef,  vanishing  at  v*h,  and  representing  the  upper  and 
lower  edges  of  the  square.  The  remainder  of  the  square  may  be 
determined  as  in  the  previous  case. 

In  a similar  manner,  the  auxiliary  line  of  measures  ml'nv 
might  have  been  used  to  determine  the  upper  and  lower  edges  of 


the  square.  This  construction  has  been  indicated,  and  the  student 
should  follow  it  through. 

59.  It  sometimes  happens  that  no  line  in  the  object  lies  in 
the  picture  plane.  In  such  a case  there  is  no  principal  line  of 
measures,  and  some  vertical  plane  in  the  object  must  be  extended 
until  it  intersects  the  picture  plane,  forming  by  this  intersection 
an  auxiliary  line  of  measures.  Fig.  21  illustrates  such  a case.  A 
rectangular  block,  similar  to  those  shown  in  Figs.  19  and  20,  is 


283 


PERSPECTIVE  DRAWING. 


situated  some  distance  behind  the  picture  plane,  as  indicated  by 
the  relative  positions  of  HPP  and  the  diagram. 

Its  perspective  projection  will  evidently  be  smaller  than  if 
the  vertical  edge  ae  were  in  the  picture  plane,  as  was  the  case  in 
Figs.  19  and  20,  and  the  perspective  of  ae  will  evidently  be 
shorter  than  the  true  length  of  ae.  There  is,  therefore,  no  line  in 
the  object  that  can  be  used  for  a line  of  measures.  It  becomes 
necessary  to  extend  one  of  the  vertical  faces  of  the  block  until  it 
intersects  the  picture  plane,  and  shows  by  the  intersection  its 
true  vertical  height.  Thus,  the  plane  abfe  has  been  extended,  as 
indicated  in  the  diagram,  until  it  intersects  the  picture  plane  in 
the  line  mn.  This  intersection  is  an  auxiliary  line  of  measures 
for  the  plane  abfe , and  mFnF  shows  the  true  vertical  height  of  this 
plane. 

Either  of  the  other  vertical  faces  of  the  block,  as  well  as  the 
face  abfe,  might  have  been  extended  until  it  intersected  the 
picture  plane,  and  formed  by  this  intersection  a line  of  measures 
for  the  block. 

The  vanishing  points  for  the  various  systems  of  lines  have 
been  found  as  in  the  previous  cases. 

From  mF  and  nF,  the  horizontal  edges  of  the  face  abfe  vanish 
to  vah.  aF  will  be  found  on  the  upper  edge  of  this  face,  vertically 
below  the  intersection  of  HPP  with  the  horizontal  projection  of 
the  visual  ray  through  the  point  a in  the  diagram.  A vertical 
line  through  aF  will  represent  the  perspective  of  the  nearest  verti- 
cal edge  of  the  block,  and  will  establish  the  position  of  eF. 

In  a similar  manner,  bF  will  be  found  vertically  below  the 
intersection  of  HPP  with  the  horizontal  projection  of  the  visual 
ray  through  the  point  b in  the  diagram.  A vertical  line  through 
bp  will  establish  fF,  and  complete  the  perspective  of  the  face  abfe. 
Having  found  the  perspective  of  this  face,  the  remainder  of  the 
block  may  be  determined  as  in  the  previous  problems. 

Note.  — Instead  of  being  some  distance  behind  the  picture 
plane,  the  block  might  have  been  wholly  or  partly  in  front  of  the 
picture  plane.  In  any  case,  find  the  intersection  with  the  picture 
plane  of  some  vertical  face  of  the  block  (produced,  if  necessary). 
This  intersection  will  show  the  true  vertical  height  of  the  block. 

At  this  point  the  student  should  solve  Plate  II. 


284 


PERSPECTIVE  DRAWING. 


33 


00.  PROBLEM  V.  Fig.  22.  To  find  the  perspective  of  a 
house,  the  projections  of  which  are  given. 

The  plan,  front,  and  side  elevations  of  the  house  are  shown 
in  the  figure.  The  side  elevation  corresponds  to  the  projection 
on  the  profile  plan,  used  in  the  study  of  projections.  This  prob- 
lem is  a further  illustration  of  the  method  of  revolved  plan  and 
of  the  use  of  horizontal  vanishing  points  and  auxiliary  lines  of 
measures.  It  is  very  similar  to  the  three  previous  problems  on 
the  rectangular  blocks. 

The  first  step  in  the  construction  of  the  perspective  projec- 
tion is  to  make  a diagram  (§  53)  which  shall  show  the  horizontal 
projections  of  all  the  features  that  are  to  appear  in  the  drawing. 
The  diagram  should  be  placed  at  the  top  of  the  sheet,  and  turned 
so  that  the  sides  of  the  house  make  the  desired  angles  with  the 
picture  plane.  In  Fig.  22  the  diagram  is  shown  with  the  long 
side  making  an  angle  of  30°  with  the  picture  plane.  The  roof 
lines,  the  chimney,  and  the  positions  of  all  windows,  doors,  etc., 
that  are  to  be  visible  in  the  perspective  projection,  will  be  seen 
marked  on  the  diagram. 

The  nearest  vertical  edge  of  the  house  is  to  lie  in  the  picture 
plane.  This  is  indicated  by  drawing  HPP  through  the  corner  of 
the  diagram  which  represents  this  nearest  edge. 

VH  may  be  chosen  at  any  convenient  distance  below  HPP. 

The  position  of  the  station  point  is  shown  in  the  figure  by 
its  two  projections  SPV  and  SPH.  SPV  must  always  be  in  VH. 
The*  distance  between  SPH  and  HPP  shows  the  distance  of  the 
observer’s  eye  in  front  of  the  picture  plane  (§  43). 

•yab  and  vad  may  be  found  as  in  the  preceding  problems. 

The  position  of  the  plane  on  which  the  object  is  to  rest 
should  next  be  established  by  drawing  VHL,  the  distance  between 
VH  and  VHj  showing  the  height  of  the  observer’s  eye  above  the 
ground  (§  44). 

In  addition  to  the  plane  of  the  ground  represented  by  VHlv 
a second  ground  plane,  represented  by  VH2,  has  been  chosen  some 
distance  below  VHj.  In  the  figure,  two  perspective  projections 
have  been  found,  one  resting  on  each  of  these  two  ground  planes. 
The  perspective  which  rests  upon  the  plane  represented  by  VIIj 
shows  the  house  as  though  seen  by  a man  standing  with  his  eyes 


285 


34 


PERSPECTIVE  DRAWING. 


nearly  on  a level  with  the  tops  of  the  windows  (§  29).  The  view 
which  rests  on  the  plane  represented  by  VH2  shows  a bird’s-eye 
view  of  the  house,  in  which  the  eye  of  the  observer  (always  in 
VH)  is  at  a distance  above  the  plane  on  which  the  view  rests, 
equal  to  about  two  and  one-half  times  the  height  of  the  ridge  of 
the  house  above  the  ground. 

The&3  two  perspective  projections  illustrate  the  effect  of 
changing  the  distance  between  VH  and  the  vertical  trace  (§  34, 
note)  of  the  plane  on  which  the  perspective  projection  is  supposed 
to  rest.  The  construction  of  both  views  is  exactly  the  same. 
The  following  explanation  applies  to  both  equally  well,  and  the 
student  may  consider  either  in  s-tudying  the  problem. 

61.  We  will  first  neglect  the  roof  of  the  house,  and  of  the 
porch.  The  remaining  portion  of  the  house  will  be  seen  to  con- 
sist of  two  rectangular  blocks,  one  representing  the  main  body  of 
the  house,  and  the  other  representing  the  porch. 

The  block  representing  the  main  part  of  the  house  occupies 
a position  exactly  similar  to  that  of  the  block  shown  in  Fig.  19. 
First  consider  this  block  irrespective  of  the  remainder  of  the 
house.  A vertical  line  dropped  from  the  corner  of  the  diagram 
that  lies  in  HPP  will  be  a measure  line  for  the  block,  and  will 
establish,  by  its  intersection  with  VH1  (or  VH2),  the  position  of 
the  point  eF,  in  exactly  the  same  way  that  the  point  eF  in  Fig.  19 
was  established.  eFaF  shows  the  true  height  of  the  part  of  the 
house  under  consideration,  and  should  be  made"  equal  to  the  cor- 
responding height  aveY,  as  shown  by  the  elevations.  The  rec- 
tangular block  representing  the  main  part  of  the  house  may  now 
be  drawn  exactly  as  was  the  block  in  Fig.  19,  Problem  IV. 

62.  Having  found  the  perspective  of  the  main  part  of  the 
house,  the  porch  (without  its  roof)  may  be  considered  as  a second 
rectangular  block,  no  vertical  edge  of  which  lies  in  the  picture 
plane.  It  may  be  treated  in  a manner  exactly  similar  to  that  of 
the  block  shown  in  Fig.  21,  § 59.  We  may  consider  that  the  rear 
vertical  face  of  the  block,  which  forms  the  porch  of  the  house 
(y,  y),  has  been  extended  until  it  intersects  the  picture  plane  in 
the  line  ae , giving  a line  of  measures  for  this  face,  just  as  in 
Fig.  21  the  nearest  vertical  face  of  the  block  was  extended  until 
it  intersected  the  picture  plane  in  the  line  of  measures  mn. 


5386 


PERSPECTIVE  DRAWING. 


On  eTav,  make  epep  equal  to  the  true  height  of  the  vertical 
wall  of  the  porch,  as  given  by  the  elevation.  A line  through  rp, 
vanishing  at  vab,  will  be  the  perspective  of  the  upper  horizontal 
edge  of  the  rear  face  of  the  block  which  forms  the  porch.  The 
line  through  ep,  vanishing  at  yab,  which  forms  the  lower  edge  of 
the  front  face  of  the  main  body  of  the  house,  also  forms  the  lower 
edge  of  the  rear  face  of  the  porch.  Through  the  point  h in  the 
diagram,  draw  a visual  ray,  and  through  the  intersection  of  this 
visual  ray  with  HPP  drop  a vertical  line.  Where  this  vertical 
line  crosses  the  upper  and  lower  horizontal  edges  of  the  rear  face 
of  the  porch,  will  establish  the  points  <jv  and  hv  respectively. 
Having  found  the  vertical  edge  gphy,  the  remainder  of  the  per- 
spective of  the  porch  (except  the  roof)  can  be  found  without 
difficulty,  the  horizontal  edges  of  the  porch  vanishing  at  either 
vab  or  according  to  the  system  to  which  they  belong.  Each 
vertical  edge  of  the  porch  will  be  vertically  below  the  point  where 
HPP  is  crossed  by  a visual  ray  drawn  through  the  point  in  the 
diagram  which  represents  that  edge.  The  fact  that  the  porch 
projects,  in  part,  in  front  of  the  picture  plane,  as  indicated  by  the 
relation  between  the  positions  of  the  diagram  and  HPP,  makes 
absolutely  no  difference  in  the  construction  of  the  perspective 
projection. 

All  of  the  vertical  construction  lines  have  not  been  shown  in 
the  figure,  as  this  would  have  made  the  drawing  too  confusing. 
The  student  should  be  sure  that  he  understands  how  every  j)oint 
in  the  perspective  projection  has  been  obtained,  and,  if  necessary, 
should  complete  the  vertical  construction  lines  with  pencil. 

63.  Having  found  the  perspective  of  the  vertical  walls  of 
the  main  body  of  the  house,  and  of  the  porch,  the  next  step  will 
be  to  consider  the  roof  of  the  main  part  of  the  house. 

Imagine  the  horizontal  line  tw,  which  forms  the  ridge  of  the 
roof,  to  be  extended  until  it  intersects  the  picture  plane.  This 
is  shown  on  the  diagram  by  the  extension  of  the  line  tw  until  it 
intersects  HPP.  From  this  intersection  drop  a vertical  line,  as 
indicated  in  the  figure.  This  vertical  line  may  be  considered  to 
be  the  line  of  measures  for  an  imaginary  vertical  plane  passing 
through  the  ridge  of  the  house,  as  indicated  by  the  dotted  lines 
in  the  plan  and  elevations  of  the  house.  On  this  line  of  meas- 


287 


PERSPECTIVE  DRAWING. 


ures,  lay  off  the  distance  nm  measured  from  YHj  (or  VII2),  equal 
to  the  true  height  of  the  ridge  above  the  ground  as  given  by  the 
elevations  of  the  house.  A line  drawn  from  the  point  m,  vanish- 
ing at  ?Pb,  will  represent  the  ridge  of  the  house,  indefinitely  ex- 
tended. From  the  points  t and  w in  the  diagram  draw  visual 
rays.  From  the  intersections  of  these  visual  rays  with  HPP 
drop  vertical  lines  which  will  establish  the  positions  of  tv  and  wv 
on  the  perspective  of  the  ridge  of  the  roof.  Lines  drawn  from 
tF  and  wv  to  the  corners  of  the  vertical  walls  of  the  house,  as  in- 
dicated, will  complete  the  perspective  of  the  roof. 

To  find  the  perspective  of  the  porch  roof,  draw  a visual  ray 
through  the  point  y on  the  diagram,  and  from  its  intersection 
with  HPP  drop  a vertical.  Where  this  vertical  crosses  the  line 
avbv  will  give  yF,  one  point  in  the  perspective  of  the  ridge  of 
the  porch.  The  perspective  of  the  ridge  will  be  represented  by 
a line  through  ?/p,  vanishing  at  vad.  The  point  zp  in  the  ridge 
will  be  vertically  below  the  intersection  of  HPP  with  the  visual 
ray  drawn  through  the  point  2 on  the  diagram.  Lines  drawn 
from  yv  and  zv  to  the  corners  of  the  vertical  walls  of  the  porch, 
as  indicated,  will  complete  the  perspective  of  the  porch  roof. 

64.  The  perspective  of  the  chimney  must  now  be  found. 
It  will  be  seen  that  the  chimney  is  formed  by  a rectangular  block ; 
and  if  it  is  supposed  to  extend  down  through  the  house,  and  rest 
upon  the  ground,  it  will  be  a block  under  exactly  the  same  con- 
ditions as  the  one  shown  in  Fig.  21,  § 59.  In  order  to  find  its 
perspective,  extend  its  front  vertical  face,  as  indicated  on  the 
diagram,  till  it  intersects  HPP.  A vertical  line  dropped  from 
this  intersection  will  be  a line  of  measures  for  the  front  face  of 
the  chimney,  and  the  distance  ps,  laid  off  on  this  line  from  VHX 
(or  YH2),  will  show  the  true  height  of  the  top  of  the  chimney  above 
the  ground,  as  given  on  the  elevation.  The  distance  so , measured 
from  the  point  s on  the  line  of  measures,  will  be  the  true  vertical 
height  of  the  face  of  the  chimney  that  is  visible  above  the  roof. 
Lines  through  s and  0 , vanishing  at  vah,  will  represent  the  hori- 
zontal edges  of  the  front  visible  face  of  the  chimney.  The  vertical 
edges  of  this  face  will  be  found  vertically  below  the  points  where 
HPP  is  crossed  by  the  visual  rays  drawn  through  the  horizontal 
projections  of  these  edges  on  the  diagram. 


288 


PERSPECTIVE  DRAWING. 


37 


Having  determined  the  perspective  of  the  front  face  of  the 
chimney,  the  perspectives  of  the  remaining  edges  may  be  found  as 
in  the  cases  of  the  rectangular  blocks  already  discussed  From 
the  point  r in  the  diagram,  where  the  ridge  of  the  roof  intersects 
the  left  hand  vertical  face  of  the  chimney,  draw  a visual  ray 
intersecting  HPP,  and  from  this  intersection  drop  a vertical  line 
to  the  perspective  of  the  ridge  of  the  house,  giving  the  perspec- 
tive (r1*)  of  the  point  where  the  ridge  intersects  the  left  hand 
face  of  the  chimney.  A line  drawn  from  rv  to  the  nearest  lower 
corner  of  the  front  face  of  the  chimney  will  be  the  perspective  of 
the  intersection  of  the  pfiane  of  the  roof  with  the  left  hand  face 
of  the  chimney. 

65.  The  problem  of  finding  the  perspectives  of  the  windows 
and  door  is  exactly  similar  to  that  of  finding  the  perspective  of 
the  square  hgkl  on  the  surface  of  the  block  shown  in  Fig.  20. 

It  wiU  be  noticed  that  the  intersection  with  the  picture  plane 
of  the  left  hand  vertical  face  of  the  porch  gives  a line  of  meas- 
ures (§55  and  § 59,  note)  for  this  face.  This  line  may  be  used 
conveniently  in  establishing  the  height  of  the  window  in  the 
porch. 

At  this  point  in  the  course  the  student  should  solve  Plate  III. 


VANISHING  POINTS  OF  OBLIQUE  LINES. 

66.  The  perspective  of  the  house  in  the  last  problem  was 
completely  drawn,  using  only  the  vanishing  points  for  the  two 
principal  systems  of  horizontal  lines.  By  this  method  it  is  pos- 
sible to  find  the  perspective  projection  of  any  object.  But  it  is 
often  advisable,  for  the  sake  of  greater  accuracy,  to  determine  the 
vanishing  p>oints  for  systems  of  oblique  lines  in  the  object,  in  addi- 
tion to  the  vanishing  points  for  the  horizontal  systems. 

Take,  for  example,  the  lines  gTyv  and  x^zv  in  Fig.  22.  The 
perspective  projections  of  these  two  lines  were  obtained  by  first 
finding  the  points  </p,  z/p,  xT,  and  2P,  and  then  connecting  </p  with  ?/p, 
and  a?  with  zv.  As  the  distances  between  g and  y,  and  x and  2, 
are  very  short,  a slight  inaccuracy  in  determining  the  positions  of 
their  perspectives  might  result  in  a very  appreciable  inaccuracy  in 
the  directions  of  the  two  lines  gvy¥  and  x?zv.  These  two  lines 


289 


38 


PERSPECTIVE  DRAWING. 


belong  to  the  same  system,  and  should  approach  one  another  as 
they  recede.  Unless  the  points  which  determine  them  are  found 
with  great  care,  the  two  lines  may  approach  too  rapidly,  or  even 
diverge,  as  they  recede  from  the  eye.  In  the  latter  case,  the 
drawing  would  be  absolutely  wrong  in  principle,  and  the  result 
would  be  very  disagreeable  to  the  trained  eye.  If,  however,  the 
perspective  of  the  vanishing  point  of  the  system  to  which  these 
two  lines  belong,  can  be  found,  and  the  two  lines  be  drawn 
to  meet  at  this  vanishing  point,  the  result  will  necessarily  be 
accurate. 

The  line  through  rp,  which  forms  the  intersection  between  the 
roof  of  the  house  and  the  left  hand  face  of  the  chimney,  is  a still 
more  difficult  one  to  determine  accurately.  Its  length  is  so  short 
that  it  is  almost  impossible  to  establish  its  exact  direction  from 
the  perspective  projections  of  its  extremities.  If  the  perspective 
of  its  vanishing  point  can  be  found,  however,  its  direction  at  once 
becomes  definitely  determined. 

67.  It  is  not  a difficult  matter  to  find  the  perspective  of  the 
vanishing  point  for  each  system  of  lines  in  an  object.  The  method 
is  illustrated  in  Fig.  23.  The  general  method  for  finding  the 
perspective  of  the  vanishing  point  for  any  system  of  lines  has 
already  been  stated  in  § 24  g , and  illustrated  in  Figs.  16,  17,  and 
18,  §§  50,  51,  and  52.  It  remains  only  to  adapt  the  general 
method  to  a particular  problem,  such  as  that  shown  in  Fig.  23. 

The  plan  and  elevation  of  a house  are  given  at  the  left  of 
the  figure.  The  diagram  has  been  drawn  at  the  top  of  the  sheet, 
turned  at  the  desired  angle.  The  assumed  position  of  the  station 
point  is  indicated  by  its  two  projections,  SPy  and  SPH.  VPI 
necessarily  passes  through  SPV. 

68.  In  order  to  find  the  perspective  of  the  vanishing  point 
of  any  system  of  lines,  the  vertical  and  horizontal  projections  of 
some  element  of  the  system  must  be  known  (see  method  of  Prob- 
lem III.).  The  diagram  gives  the  horizontal  projection  of  every 
line  in  the  object  which  is  to  appear  in  the  perspective  projection. 
The  diagram,  however,  has  been  turned  through  a certain  hori- 
zontal angle  in  order  to  show  the  desired  perspective  view,  and 
there  is  no  revolved  elevation  to  agree  with  the  revolved  position 
of  the  diagram.  A revolved  elevation  could,  of  course,  be  con- 


290 


HPP 


PERSPECTIVE  DRAWING. 


39 


structed  by  revolving  the  given  plan  of  the  object  until  all  its 
lines  were  parallel  to  the  corresponding  lines  in  the  diagram,  and 
then  finding  the  revolved  elevation  of  the  object  corresponding  to 
the  revolved  position  of  the  plan. 

Note.  — The  method  of  constructing  a revolved  elevation 
has  been  explained  in  detail  in  the  Instruction  Paper  on  Mechan- 
ical Drawing,  Part  III.,  Page  12. 

Having  constructed  the  revolved  plan  and  elevation  of  the 
object  to  agree  with  the  position  of  the  diagram,  we  should  then 
have  the  vertical  and  horizontal  projections  of  a line  parallel  to 
each  line  that  is  to  appear  in  the  perspective  drawing,  and  the 
method  of  Problem  III.  could  be  applied  directly. 

This  is  exactly  the  process  that  will  be  followed  in  finding 
the  vanishing  points  for  the  oblique  lines  in  the  object,  except 
that  instead  of  making  a complete  revolved  plan  and  elevation 
of  the  house,  each  system  of  lines  will  be  considered  by  itself, 
and  the  revolved  plan  and  elevation  of  each  line  will  be  found 
as  it  is  needed,  without  regard  to  the  remaining  lines  in  the 
object. 

69.  All  the  lines  in  the  house  belong  to  one  of  eleven 
different  systems  that  may  be  described  as  follows : — 

A vertical  system,  to  which  all  the  vertical  lines  in  the  house 
belong.  The  perspective  of  the  vanishing  point  of  this 
system  cannot  be  found  within  finite  limits  (§  54). 

Two  horizontal  systems  parallel  respectively  to  ah  and  ad 
(see  diagram).  The  perspectives  of  the  vanishing  points 
of  these  systems  will  be  found  in  YH  (§  24  c,  note). 

Five  systems  of  lines  vanishing  upward,  parallel  respectively  to 
af,  bg , mn , on,  and  lik  (see  diagram).  The  perspectives  of 
the  vanishing  points  of  these  systems  will  be  found  to  lie 
above  YH  (§  51,  note). 


293 


40 


PERSPECTIVE  DRAWING. 


Three  systems  of  lines  vanishing  downward,  parallel  respec- 
tively to  fd , gc,  and  kl  (see  diagram).  The  perspectives 
of  the  vanishing  points  of  these  systems  will  he  found  be- 
low YII  (§  51,  note). 


NOTE.  — To  determine  whether  a line  vanishes  upward  or 
downward,  proceed  as  follows  : 


Examine  the  direction  of  the  line  as  shown  in  the  dia- 
gram. Determine  which  end  of  the  line  is  the  farther  behind 
the  picture  plane.  If  the  more  distant  end  of  the  line  is  above 
the  nearer  end,  the  line  vanishes  upward,  and  the  perspective 
of  its  vanishing  point  will  be  found  above  VH. 

If,  on  the  other  hand,  the  more  distant  end  of  the  line 
is  lower  than  the  nearer  end,  the  line  vanishes  downward , and 
the  perspective  of  its  vanishing  point  will  be  found  below 
VH. 

For  illustration,  consider  the  line  bg.  The  diagram  shows 
the  point  g to  be  farther  behind  the  picture  plane  than  the  point 
b,  while  the  given  elevation  shows  the  point  g to  be  higher  than, 
the  point  b.  Therefore  the  line  rises  as  it  recedes , or,  in  other 
words,  it  vanishes  upward. 

In  the  case  of  the  line  fd,  the  diagram  shows  the  point  d to 
be  farther  behind  the  picture  plane  than  the  point  f,  while  the 
elevation  shows  the  point  d to  be  lower  than  the  point  f.  There- 
fore the  line  must  vanish  downward,  and  its  vanishing  point  be 
found  below  VIT. 

If  the  horizontal  projection  of  a line,  as  shown  by  the  dia- 
gram, is  parallel  to  1 1 P P,  the  line  itself  is  parallel  to  the  picture 
plane,  and  the  perspective  of  its  vanishing  point  cannot  be  found 
within  finite  limits  (§  54,  note).  The  perspective  projections  of  such  a 


294 


PERSPECTIVE  DRAWING. 


41 


system  of  lines  will  show  the  true  angle  which  the  elements  of  the 
system  make  with  the  horizontal  coordinate . 

70.  The  construction  for  the  vanishing  points  in  Fig.  23  is 
shown  by  dot  and  dash  lines. 

The  vanishing  points  for  the  two  systems  of  horizontal  lines 
have  been  found  at  vab  and  vad  respectively,  as  in  the  preceding 
problems. 

Next  consider  the  line  af.  The  first  step  is  to  construct  a 
revolved  plan  and  elevation  of  this  line  to  agree  with  the  position 
of  the  diagram.  Revolve  the  horizontal  projection  (a11/11)  of  the 
line  in  the  given  plan  about  the  point /H,  until  it  is  parallel  to  the 
line  af  in  the  diagram.  During  this  revolution,  the  point  fK 
remains  stationary,  while  the  point  aK  describes  a horizontal  arc, 
until  off11  has  revolved  into  the  position  shown  by  the  red  line 
a\ H/H?  which  is  parallel  to  the  line  af  in  the  diagram.  The  vertical 
projection  aYfv  must,  of  course,  revolve  with  the  horizontal  projec- 
tion. The  point  /v  remains  stationary,  while  the  horizontal  arc 
described  by  the  point  a shows  in  vertical  projection  as  a horizon- 
tal line.  At  every  point  of  the  revolution  the  vertical  projection 
of  the  point  a must  be  vertically  in  line  with  its  horizontal  pro- 
jection. A\rhen  aR  has  reached  the  position  af,  ay  will  be  vertically 
above  af  at  the  point  af  and  affy  will  be  the  revolved  elevation 
of  the  line. 

We  now  have  the  vertical  and  horizontal,  projections  (affY 
and  aRfR)  of  an  element  of  the  system  to  which  the  roof  line,  rep- 
resented in  the  diagram  by  af  belongs.  The  vanishing  point  of  this 
system  may  be  determined  as  in  Problem  III.  Draw  through 
SPH  a line  parallel  to  affH  (or  af  in  the  diagram),  representing 
the  horizontal  projection  of  the  visual  element  of  the  system. 
Draw  through  SPV  a line  parallel  to  aYfY,  representing  the  verti- 
cal projection  of  the  visual  element  of  the  system.  The  visual 
element,  represented  by  the  two  projections  just  drawn,  pierces 
the  picture  plane  at  vaf  (§  45,  note),  giving  the  perspective  of 
the  vanishing  point  for  the  roof  line,  represented  by  af  in  the 
diagram. 

In  a similar  manner  the  vanishing  point  for  the  roof  line, 
represented  in  the  diagram  by  by,  may  be  determined.  First  find, 
from  the  given  plan  and  elevation  of  the  object,  a revolved  plan 


295 


42 


PERSPECTIVE  DRAWING. 


and  elevation  of  bg,  to  agree  with  the  position  of  the  line  in  the 
diagram.  Revolve  bugu  in  the  given  plan  about  the  point  gn, 
until  it  is  parallel  to  bg  in  the  diagram,  and  occupies  the  position 
indicated  by  the  line  bfgn.  The  corresponding  revolved  elevation 
is  represented  by  the  red  line  b^gy. 

bfg11  and  blYgY  now  represent  respectively  the  horizontal 
and  vertical  projections  of  an  element  of  the  system  to  which  the 
roof  line,  represented  by  bg  in  the  diagram,  belongs.  The  vanish- 
ing point  of  this  system  can  be  found  by  Problem  III.  Through 
SPH  draw  a line  parallel  to  b^g™  (or  bg  in  the  diagram),  repre- 
senting the  horizontal  projection  of  the  visual  element  of  the  sys- 
tem ; and  through  SPV  draw  a line  parallel  to  bfgY,  representing 
the  vertical  projection  of  their  visual  element.  The  visual  ele- 
ment, represented  by  these  two  projections,  pierces  the  picture 
plane  at  vbg,  giving  the  perspective  of  the  vanishing  point  of  the 
roof  line,  represented  in  the  diagram  by  the  line  bg. 

By  a similar  process,  hPkjf-  and  liYkY  are  found  to  represent 
respectively  the  horizontal  and  vertical  projections  of  an  element 
of  the  system  to  which  belongs  the  roof  line  represented  in  the 
diagram  by  the  line  hk.  The  perspective  of  the  vanishing  point 
of  this  line  has  been  found  at  vhk. 

vaf,  vhg,  and  vhk  have  all  been  found  to  lie  above  VH  (§51. 
note). 

71.  vm,  vgc,  and  vkl  are  found  exactly  as  were  #af,  vhg, 
and  vhk ; but,  as  the  systems  to  which  they  belong  vanish  down- 
ward, they  will  lie  below  VH  (§  51,  note). 

Thus,  /Hc?iH  and  fYdY  are  respectively  the  horizontal  and 
vertical  projections  of  an  element  of  the  system  represented  by  fd 
in  the  diagram.  A line  drawn  through  SPH,  parallel  to f^d™  (or 
fd  in  the  diagram),  will  intersect  HPP  in  the  point  w.  A verti- 
cal line  through  w will  intersect  a line  through  SPV  parallel  to 
fYdY,  below  VH. 

72.  Having  found  the  perspectives  of  these  vanishing  points, 
the  perspectives  of  the  vanishing  traces  of  all  the  planes  in  the 
object  should  be  drawn  as  a test  of  the  accuracy  with  which  the 
vanishing  points  have  been  (Constructed.  The  roof  planes  in 
the  house  are  lettered  with  the  capital  letters  M,  N,  O,  P,  etc., 
on  the  diagram. 


296 


'HA 


PERSPECTIVE  DRAWING. 


43 


The  plane  O contains  the  lines  af,  ad , and  fd.  Therefore,  the 
vanishing  trace  (TO)  of  the  plane  must  be  a straight  line  passing 
through  the  three  vanishing  points,  vaf,  i>ad,  and  vfd  (§  24  d).  Jf 
all  three  of  these  vanishing  points  do  not  lie  in  a straight  line,  it 
shows  some  inaccuracy,  either  in  draughting  or  in  the  method 
used  in  finding  some  of  the  vanishing  points.  The  student  should 
not  be  content  until  the  accuracy  of  his  work  is  proved  by  draw- 
ing the  vanishing  trace  of  each  plane  in  the  object  through  the 
vanishing  points  of  all  lines  that  lie  in  that  plane. 

The  plane  M contains  the  lines  fd,  gc,  and  do.  The  last  line 
belongs  to  the  system  ab,  and  hence  its  vanishing  point  is  v'Ah. 
The  vanishing  trace  (TM)  of  the  plane  M must  pass  through  v{d, 
vgc , and  vab. 

Similarly,  the  vanishing  trace  (TP)  of  the  plane  P must  pass 
through  vgc , t>bg,  and  vRd.  TN  must  pass  through  vab,  vaf,  and  vhg. 
TQ  must  pass  through  vhk  and  t;ad.  TR  must  pass  through  vkl 
and  vAd. 

73.  The  vanishing  trace  of  a vertical  plane  will  always  be  a 
vertical  line  passing  through  the  vanishing  points  of  all  lines 
which  lie  in  the  plane.  Therefore,  the  vanishing  trace  of  the 
vertical  planes  in  the  house  that  vanish  towards  the  left  will  be 
represented  by  a vertical  line  (TS)  passing  through  vAd. 

The  vanishing  trace  of  the  vertical  planes  of  the  house  that 
vanish  towards  the  right  will  be  represented  by  a vertical  line 
(TT)  passing  through  yab.  As  the  vertical  plane  which  forms 
the  face  of  the  porch  belongs  to  this  system,  and  as  this  plane 
also  contains  the  lines  hk  and  Id , TT  will  be  found  to  pass 
through  vhk  and  vkl  as  well  as  vab. 

74.  It  will  be  noticed  that  the  vanishing  points  for  the  lines 
mn  and  on  have  not  been  found.  These  vanishing  points  might 
have  been  found  in  a manner  exactly  similar  to  that  in  which  the 
other  vanishing  points  were  found,  or  they  may  be  determined 
now,  directly  from  the  vanishing  traces  already  drawn,  in  the 
following  manner : — 

The  line  mn  is  seen  to  be  the  line  of  intersection  of  the  two 
planes  N and  Q.  Therefore  (§  24  e)  vmn  must  lie  at  the  inter- 
section of  TN  and  TQ. 

For  a similar  reason,  von  must  lie  at  the  intersection  of  TN 


299 


44 


PERSPECTIVE  DRAWING. 


and  TR.  TN  and  TR  do  not  intersect  within  the  limits  of  the 
plate,  but  they  are  seen  to  converge  as  they  pass  to  the  ieft,  and, 
if  produced  in  that  direction,  would  meet  at  the  vanishing  point 
for  the  line  on. 

T5.  Having  found  vab,  vad,  vbg,  and  vm,  TN  could  have  been 
drawn  through  vab  and  vbg;  and  TO  could  have  been  drawn 
through  vad  and  vfd.  As  af  is  the  intersection  of  the  two  planes 
N and  O,  vaf  could  have  been  found  at  the  intersection  of  TN  and 
TO  without  actually  constructing  this  vanishing  point. 

Similarly,  vgG  could  have  been  determined  by  the  intersec- 
tion of  TM  and  TP. 

By  an  examination  of  the  plate,  the  student  will  notice  that 
the  vanishing  point  for  each  line  in  the  object  is  formed  at  the 
intersection  of  the  vanishing  traces  of  the  two  planes  of  which 
the  line  forms  the  intersection.  Thus,  the  line  ad  forms  the  inter- 
section between  the  plane  O and  the  left  hand  vertical  face  of  the 
house.  vad  is  found  at  the  intersection  of  TO  and  TS. 

The  line  fg , which  forms  the  ridge  of  the  roof,  is  the  inter- 
section of  the  planes  M and  N.  The  vanishing  point  for  fg  is 
vab,  and  TM  and  TN  will  be  found  to  intersect  at  v*h.  vbk  is 
found  at  the  intersection  of  TQ  and  TT,  rkl  is  found  at  the  inter- 
section of  TR  and  TT,  etc. 

It  will  be  noticed  also  that  the  two  lines  hk  and  kl  lie  in  the 
same  vertical  plane,  and  make  the  same  angle  with  the  horizontal, 
one  vanishing  upward,  and  one  vanishing  downward.  Since  both 
lines  lie  in  the  same  vertical  plane,  both  of  their  vanishing  points 
will  be  found  in  the  vertical  line  which  represents  the  vanishing 
trace  of  that  plane.  Also,  since  both  lines  make  equal  angles  with 
the  horizontal,  the  vanishing  point  of  the  line  vanishing  upward 
will  be  found  as  far  above  VH  as  the  vanishing  point  of  the  line 
vanishing  downward  is  below  VH. 

In  a similar  way,  the  line  bg  vanishes  upward,  and  the  line 
fd  vanishes  downward ; each  making  the  same  angle  with  the 
horizontal  (as  shown  by  the  given  plan  and  elevation).  These 
two  lines  do  not  lie  in  the  same  plane,  but  may  be  said  to  lie  in 
two  imaginary  vertical  planes  which  are  parallel  to  one  another. 
Their  vanishing  points  will  be  seen  to  lie  in  the  same  vertical  line, 
vhg  being  as  far  above  VH  as  ^fd  is  below  it. 


300 


PERSPECTIVE  DRAWING 


45 


As  a general  statement,  it  may  be  said  that  if  two  lines  lie 
in  the  same  or  parallel  vertical  planes,  and  make  equal  angles 
with  the  horizontal,  one  vanishing  upward  and  the  other  van- 
ishing downward,  the  vanishing  points  for  both  lines  will  be 
found  vertically  in  line  with  one  another,  one  as  far  above 
VH  as  the  other  is  below  it. 

This  principle  is  often  of  use  in  constructing  the  vanishing 
point  diagram.  Thus,  having  found  Flk,  vkl  could  have  been 
determined  immediately  by  making  it  lie  in  a vertical  line  with 
Flk,  and  as  far  below  VH  as  Flk  is  above  it. 

VANISHING  POINT  DIAGRAM. 

76.  The  somewhat  symmetrical  figure  formed  by  the  vanish- 
ing traces  of  all  the  planes  in  the  object,  together  with  all 
vanishing  points,  HPP,  and  the  vertical  and  horizontal  projec- 
tions of  the  station  point,  is  called  the  Vanishing  Point  Diagram 
of  the  object. 

77.  Having  found  the  complete  vanishing  point  diagram  of 
the  house,  the  perspective  projection  may  be  drawn.  VHt  may 
be  chosen  in  accordance  with  the  kind  of  a perspective  projection 
it  is  desired  to  produce  (§  29).  In  order  that  all  the  roof  lines 
may  be  visible,  VHj  has  been  chosen  far  below  VH.  The  result- 
ing perspective  is  a somewhat  exaggerated  bird’s-eye  view. 

The  point  ep  will  be  found  on  VIR,  vertically  under  the 
point  e in  the  diagram.  apep  lies  in  the  picture  plane,  and  shows 
the  true  height  of  the  vertical  wall  of  the  house.  From  av  and 
ep,  the  horizontal  edges  of  the  walls  of  the  main  house  vanish  to 
v'Ah  and  vad. 

The  points  dp,  bp , mp,  and  op  are  found  on  the  upper  hori- 
zontal edges  of  the  main  walls,  vertically  under  the  points  where 
HPP  is  crossed  by  visual  rays  drawn  through  the  points  c?,  b,  m , 
and  o in  the  diagram.  Vertical  lines  from  dp  and  bp  complete 
the  visible  vertical  edges  of  the  main  house. 

In  a similar  manner  the  perspective  of  the  vertical  walls  of 
the  porch  is  obtained. 

Each  roof  line  vanishes  to  its  respective  vanishing  point. 
apfp  vanishes  at  vat.  fpdp  vanishes  at  vfd.  These  two  lines  inter- 


301 


46 


PERSPECTIVE  DRAWING. 


sect  in  the  point /p.  The  ridge  of  the  main  house  passes  through 
fp , vanishing  at  ^ab.  gpcp  vanishes  at  vgc,  passing  through  the 
point  cp,  which  has  already  been  determined  by  the  intersection 
of  the  two  upper  rear  horizontal  edges  of  the  main  walls.  bpgp 
vanishes  at  vhs , completing  the  perspective  of  the  main  roof. 

In  the  porch,  hpkp  vanishes  at  Flk,  passing  through  the  point 
Ap,  already  determined  by  the  vertical  walls  of  the  porch.  kplp 
passes  through  lp,  and  vanishes  at  vkl.  From  k?  the  ridge  of  the 
porch  roof  vanishes  at  vad.  From  mp,  a line  vanishing  at  vmn 
will  intersect  the  ridge  in  the  point  wp,  and  represent  the  intersec- 
tion of  the  roof  planes  Q and  N.  The  vanishing  point  for  opnp 
falls  outside  the  limits  of  the  plate.  opmp  may  be  connected  with 
a line  which,  if  the  drawing  is  accurate,  will  converge  towards 
both  TN  and  TR,  and,  if  produced,  would  meet  them  at  their 
intersection. 

78.  While  constructing  the  vanishing  point  diagram  of  an 
object,  the  student  should  constantly  keep  in  mind  the  general 
statements  made  in  the  note  under  § 69. 

Plate  IV.  should  now  be  solved. 


PARALLEL  OR  ONE=POINT  PERSPECTIVE. 

79.  When  the  diagram  of  an  object  is  placed  with  one  of  its 
principal  systems  of  horizontal  lines  parallel  to  the  picture  plane, 
it  is  said  to  be  in  Parallel  Perspective.  This  is  illustrated  in 
Fig.  24,  by  the  rectangular  block  there  shown.  One  system  of 
horizontal  lines  in  the  block  being  parallel  to  the  picture  plane, 
the  other  system  of  horizontal  lines  must  be  perpendicular  to  the 
picture  plane.  The  vanishing  point  for  the  latter  system  will  be 
coincident  with  SPV  (§  52).  The  horizontal  system  that  is  parallel 
to  the  picture  plane  will  have  no  vanishing  point  within  finite 
limits  (§  54,  with  note ; also  last  paragraph  of  note  under  § 69). 
The  third  system  of  lines  in  the  object  is  a vertical  one,  and  will 
have  no  vanishing  point  within  finite  limits  (§  54).  Thus,  of  the 
three  systems  of  lines  that  form  the  edges  of  the  block,  only  one 
will  have  a vanishing  point  within  finite  limits.  This  fact  has 
led  to  the  term  One-Point  Perspective,  which  is  often  applied  to 
an  object  in  the  position  shown  in  Fig.  24.  As  will  be  seen,  this 


302 


47 


PERSPECTIVE 


DRAWING. 


is  only  a special  case  of  the  problems  already  studied,  and  the 
construction  of  the  perspective  of  an  object  in  parallel  perspective 
is  usually  simpler  than  when  the  diagram  is  turned  at  an  angle 
with  HPP. 

80.  The  vertical  face  ( abfe ) of  the  block  lies  in  the  picture 
plane.  It  will  thus  show  in  its  true  size  and  shape  (§  24  A).  The 


points  ep  and  /p  will  be  found  on  VHj  vertically  below  the  points 
e and /in  the  diagram. 

81.  Both  the  edges  eTav  and  flbv  are  lines  of  measures,  and 
will  show  the  true  height  of  the  block,  as  given  by  the  elevation. 

82.  The  two  lines  avbp  and  <?p/p,  since  they  are  formed  by 
the  intersection  of  the  bases  of  the  block  with  the  picture  plane, 
will  also  be  lines  of  measures  (§  55),  and  will  show  the  true 
length  of  the  block,  as  given  by  the  plan  and  elevation. 

88.  The  perspective  of  the  front  face  of  the  block,  which  is 


303 


48 


PERSPECTIVE  DRAWING. 


coincident  with  the  picture  plane,  can  be  drawn  immediately. 
From  aF,  />p,  eF , and  /p,  the  horizontal  edges,  which  are  perpendicu- 
lar to  the  picture  plane,  will  vanish  at  vad  (coincident  with  SPV). 
The  rear  vertical  edges  of  the  block  may  be  found  in  the  usual 
manner. 

84.  The  lines  apbF,  dFcp , epfF,  and  hFgF,  which  form  the  hori- 
zontal edges  parallel  to  the  picture  plane,  will  all  be  drawn  paral- 
lel to  one  another  (§  54,  note)  ; and  since  the  lines  in  space  which 
they  represent  are  horizontal,  ap6p,  dFcp,  erfp , and  hFgF  will  all 
be  horizontal  (see  last  paragraph  of  note  under  § 69). 

All  of  the  principles  that  have  been  stated  in  connection  with 
the  other  problems  will  apply  equally  well  to  an  object  in  parallel 
perspective. 

85.  Interior  views  are  often  shown  in  parallel  perspective. 
One  wall  of  the  interior  is  usually  assumed  coincident  with  the 
picture  plane,  and  is  not  shown  in  the  drawing.  For  illustration, 
the  rectangular  block  in  Fig.  24  may  be  considered  to  represent  a 
hollow  box,  the  interior  of  which  is  to  be  shown  in  perspective. 
Assume  the  face  ( avbvfvev ) that  lies  in  the  picture  plane  to  be 
removed.  The  resulting  perspective  projection  would  show  the 
interior  of  the  box.  In  making  a parallel  perspective  of  an  interior, 
however,  VH  is  usually  drawn  lower  than  is  indicated  in  Fig.  24, 
in  order  to  show  the  inside  of  the  upper  face,  or  ceiling,  of  the 
interior.  With  such  an  arrangement,  three  walls,  the  ceiling,  and 
the  floor  of  the  interior,  may  all  be  shown  in  the  perspective 
projection. 

86.  Fig.  25  shows  an  example  of  interior  parallel  perspective. 
The  plan  of  the  room  is  shown  at  the  top  of  the  plate.  This  has 
been  placed  so  that  it  may  be  used  for  the  diagram,  and  save  the 
necessity  of  making  a separate  drawing.  The  elevation  of  the 
room  is  shown  at  the  left  of  the  plate,  and  for  convenience  it  has 
been  placed  with  its  lower  horizontal  edge  in  line  with  VHj.  In 
this  position  all  vertical  dimensions  in  the  object  may  be  carried 
by  horizontal  construction  lines  directly  from  the  elevation  to 
the  vertical  line  of  measures  (aFep  or  bpfF>)  in  the  perspective 
projection. 

87.  The  front  face  of  the  room  ( 'avbvf*eF)f  which  is  coinci- 
dent with  the  picture  plane,  may  first  be  established.  Each  point 


304 


PERSPECTIVE  DRAWING. 


49 


in  the  perspective  of  this  front  face  will  he  found  to  lie  vertically 
under  the  corresponding  point  in  plan,  and  horizontally  in  line 
with  the  corresponding  point  in  elevation.  Thus,  aF  is  vertically 
under  an , and  horizontally  in  line  with  ay. 

All  lines  in  the  room  which  are  perpendicular  to  the  picture 
plane  vanish  at  vad  (coincident  with  SPV). 

Drawing  visual  rays  from  every  point  in  the  diagram,  the 
corresponding  points  in  the  perspective  projection  will  be  verti- 
cally under  the  points  where  these  visual  rays  intersect  HPP. 
The  construction  of  the  walls  of  the  room  should  give  the  student 
no  difficulty. 

88.  In  finding  the  perspective  of  the  steps,  the  vertical 
heights  should  first  be  projected  by  horizontal  construction  lines 
from  the  elevation  to  the  line  of  measures  (apep),  as  indicated  by 
the  divisions  between  eF  and  m.  These  divisions  can  then  be 
carried  along  the  left  hand  wall  of  the  room  by  imaginary  hori- 
zontal lines  vanishing  at  vad.  The  perspective  of  the  vertical 
edge  where  each  step  intersects  the  left  hand  wall  may  now  be 
determined  from  the  plan.  Thus,  the  edge  s?rp  of  the  first  step 
is  vertically  below  the  intersection  of  HPP  with  a visual  ray 
drawn  through  the  point  sH  in  plan,  and  is  between  the  two  hori- 
zontal lines  projected  from  the  elevation  that  show  the  height  of 
the  lower  step.  The  corresponding  vertical  edge  of  the  second 
step  will  be  projected  from  the  plan  in  a similar  manner,  and  will 
lie  between  the  two  horizontal  lines  projected  from  the  elevation 
that  show  the  height  of  the  second  step,  etc. 

From  sF  the  line  which  forms  the  intersection  of  the  wall 
with  the  horizontal  surface  of  the  first  step  will  vanish  to  t,ad,  etc. 

From  rF  the  intersection  of  the  first  step  with  the  floor  of  the 
room  will  be  a line  belonging  to  the  same  system  as  aFbF,  and  will 
therefore  show  as  a true  horizontal  line.  The  point  tF  may  be 
projected  from  the  diagram  by  a visual  ray,  as  usual.  From  tF  the 
vertical  edge  of  the  step  may  be  drawm  till  it  intersects  a horizon- 
tal line  through  sr , and  so  on,  until  the  steps  that  rest  against  the 
side  wall  are  determined. 

89.  The  three  upper  steps  in  the  flight  rest  against  the  rear 
wall.  The  three  upper  divisions  on  the  line  e?m  may  be  carried 
along  the  left  hand  wall  of  the  room,  as  indicated,  till  they  inter- 


305 


50 


PERSPECTIVE  DRAWING. 


sect  the  rear  vertical  edge  of  the  wall,  represented  by  the  line 
dThF.  From  these  intersections  the  lines  may  he  carried  along 
the  rear  wall  of  the  room,  showing  the  heights  of  the  three  upper 
steps  where  they  rest  against  the  rear  wall. 

The  three  upper  divisions  on  the  line  evm  have  also  been 
projected  across  to  the  line  frbv,  and  from  this  line  carried  by 
imaginary  horizontal  lines  along  the  right  hand  wall  of  the  room 
to  the  plane  N,  across  the  plane  N to  the  plane  O,  and  from  the 
plane  O to  the  plane  M.  Thus,  for  illustration,  the  upper  division, 
representing  the  height  of  the  upper  step,  has  been  carried  from 
rn  toe;  from  c to  g along  the  right  hand  face  of  the  wall; 
from  g to  j along  the  plane  N ; from  j to  k on  the  plane  O,  and 
from  k to  pv  on  the  plane  M. 

The  jDoint  pv  is  where  the  line  which  represents  the  height  of 
the  upper  step  meets  a vertical  dropped  from  the  intersection  of 
HPP  with  a visual  ray  through  the  point  pH  in  the  diagram.  pv 
is  one  corner  in  the  perspective  of  the  upper  step,  the  visible  edges 
of  the  step  being  represented  by  a horizontal  line,  pvk , a line 
(y>pop)  vanishing  at  v'Ad,  and  a vertical  line  drawn  from  pT  between 
the  two  horizontal  lines  on  the  plane  11,  which  represent  the 
height  of  the  upper  step.  The  point  oT  is  at  the  intersection  of 
the  line  drawn  through  y>p,  vanishing  through  vad,  with  the  hori- 
zontal line  on  the  rear  wall  drawn  through  the  point  n , and 
representing  the  upper  step  where  it  rests  against  the  rear 
wall. 

The  remaining  steps  may  be  found  in  a similar  manner.  The 
student  should  have  no  difficulty  in  following  out  the  construction, 
which  is  all  shown  on  the  plate. 

90.  The  position  of  the  point  tv  on  the  line  rvtv  was  deter- 
mined by  projecting  in  the  usual  manner  from  the  diagram.  The 
position  of  tv  might  have  been  found  in  the  following  manner : In 
the  figure  the  line  eFfF  is  a line  of  measures  (§  81),  and  divisions 
on  this  line  will  show  in  their  true  size.  Thus,  if  we  imagine  a 
horizontal  line  to  be  drawn  through  £p,  parallel  to  the  wall  of  the 
room,  it  will  intersect  eTfT  in  the  point  u.  Since  eTu  is  on  a line 
of  measures,  it  will  show  in  its  true  length.  Thus,  tF  might  have 
been  determined  by  laying  off  evu  equal  to  the  distance  eH?q  taken 
from  the  plan,  and  then  drawing  through  the  point  u a line  van- 


306 


* 


PERSPECTI VE  DRAWING. 


isliing  at  vad.  The  intersection  of  this  line  with  the  horizontal 
line  drawn  through  rv  will  determine  tv. 

In  a similar  manner  the  vertical  edges  of  the  steps,  where 
they  intersect  the  plane  M,  might  have  been  found  by  laying  off 
from  u,  on  evfv,  the  divisions  uv  and  vw  taken  from  the  plan. 
These  divisions  could  have  been  carried  along  the  floor  by  hori- 
zontal lines  parallel  to  the  sides  of  the  room  (vanishing  at  vad),  to 
the  plane  M,  and  then  projected  vertically  upward  on  the  plane 
M,  as  indicated  in  the  figure. 

Solve  Plate  Y. 

METHOD  OF  PERSPECTIVE  PLAN. 

91.  In  the  foregoing  problems  the  perspective  projection  has 
been  found  from  a diagram  of  the  object.  Another  way  of  con- 
structing a perspective  projection  is  by  the  method  of  Perspective 
Plan.  In  this  method  no  diagram  is  used,  but  a perspective  plan 
of  the  object  is  first  made,  and  from  this  perspective  plan  the  per- 
spective projection  of  the  object  is  determined.  The  perspective 
plan  is  usually  supposed  to  lie  in  an  auxiliary  horizontal  plane 
below  the  plane  of  the  ground.  The  principles  upon  which  its 
construction  is  based  will  now  be  explained. 

92.  In  Fig.  26,  suppose  the  rectangle  aHbHcHdH  to  represent 
the  horizontal  projection  of  a rectangular  card  resting  upon  a 
horizontal  plane.  The  diagram  of  the  card  is  shown  at  the  upper 
part  of  the  figure.  It  will  be  used  only  to  explain  the  construc- 
tion of  the  perspective  plan  of  the  card. 

First  consider  the  line  ad , which  forms  one  side  of  the  card. 
On  HPP  lay  off  from  a , to  the  left,  a distance  ( ae ) equal  to  the 
length  of  the  line  ad.  Connect  the  points  e and  d.  ead  is  by 
construction  an  isosceles  triangle  lying  in  the  plane  of  the  card, 
with  one  of  its  equal  sides  ( ae ) in  the  picture  plane.  Now,  if  this 
triangle  be  put  into  perspective,  the  side  ad,  being  behind  the  pic- 
ture plane,  will  appear  shorter  than  it  really  is ; while  the  side  ae, 
which  lies  in  the  picture  plane,  will  show  in  its  true  length. 

Let  VHj  be  the  vertical  trace  of  the  plane  on  which  the  card 
and  triangle  are  supposed  to  rest.  The  position  of  the  station 
point  is  shown  by  its  two  projections  SPH  and  SPY  The  vanish- 


309 


52 


PERSPECTIVE  DRAWING. 


ing  point  for  the  line  ad  will  be  found  at  vad  in  the  usual  man- 
ner. In  a similar  way,  the  Vanishing  point  for  the  line  ed , which 
forms  the  base  of  the  isosceles  triangle,  will  be  found  at  ved , as 
indicated.  av  will  be  found  on  YHj  vertically  under  the  point  a, 
which  forms  the  apex  of  the  isosceles  triangle  ead.  The  line 
avdF  will  vanish  at  vad.  The  point  eF  will  be  found  vertically 


below  the  point  e.  epdp  will  vanish  at  vetl,  and  determine  by  its 
intersection  with  avdp  the  length  of  that  line.  epapdp  is  the 
perspective  of  the  isosceles  triangle  ead. 

If  the  line  ad  in  the  diagram  is  divided  in  any  manner  by 
the  points  t,  s,  and  r,  the  perspectives  of  these  points  may  be 
found  on  the  line  apdp  in  the  following  way.  If  lines  are  drawn 


310 


PERSPECTIVE  DRAWING. 


through  the  points  t,  s,  and  r in  the  diagram  parallel  to  the  base 
de  of  the  isosceles  triangle  ( ead ),  these  lines  will  divide  the  line 
ae  in  a manner  exactly  similar  to  that  in  which  the  line  ad  is  di- 
vided. Thus,  aw  will  equal  at , wv  will  equal  ts,  etc.  Now,  in  the 
perspective  projection  of  the  isosceles  triangle,  apep  lies  in  the 
picture  plane.  It  will  show  in  its  true  length,  and  all  divisions 
on  it  will  show  in  their  true  size.  Thus,  on  apep  lay  off  apwp, 
ivpvp , and  vpup  equal  to  the  corresponding  distances  at , ts,  and  $>% 
given  in  the  diagram.  Lines  drawn  through  the  points  ivp,  vp , 
and  up,  vanishing  at  ved , will  be  the  perspective  of  the  lines  wt , 
vs , and  ur  in  the  isosceles  triangle,  and  will  determine  the  positions 
of  tp,  sp,  and  rp,  by  their  intersections  with  apdp. 

93.  It  will  be  seen  that  after  having  found  rad  and  ved,  the 
perspective  of  the  isosceles  triangle  can  be  found  without  any 
reference  to  the  diagram.  Assuming  the  position  of  ap  at  any 
desired  point  on  VHj,  the  divisions  ap,  wp , vp,  up , ep  may  be  laid  off 
from  ap  directly,  making  them  equal  to  the  corresponding  divisions 
«H,  tH,  s11,  rH,  dn,  given  in  the  plan  of  the  card.  A line  through  ap 
vanishing  at  vad  will  represent  the  perspective  side  of  the  isosceles 
triangle.  The  length  of  this  side  will  be  determined  by  a line 
drawn  through  ep,  vanishing  at  ved.  The  positions  of  tp,  sp,  and 
rF  may  be  determined  by  lines  drawn  through  wp , vp,  and  up , van- 
ishing at  ved. 

94.  It  will  be  seen  that  the  lines  drawn  to  red  serve  to 
measure  the  perspective  distances  ap  tp , tp  sp,  sp  rp,  and  rp  dF,  on 
the  line  apdp,  from  the  true  lengths  of  these  distances  as  laid  off 
on  the  line  apep.  Hence  the  lines  vanishing  at  ved  are  called 
Measure  Lines  for  the  line  apdp,  and  the  vanishing  point  vedis 
called  a Measure  Point  for  apdp. 

95.  Every  line  in  perspective  has  a measure  point,  which 
may  be  found  by  constructing  an  isosceles  triangle  on  the  line  in  a 
manner  similar  to  that  just  explained. 

Note.  - — The  vanishing  point  for  the  base  of  the  isosceles 
triangle  always  becomes  the  measure  point  for  the  side  of  the 
isosceles  triangle  which  does  not  lie  in  HPP. 

96.  All  lines  belonging  to  the  same  system  will  have  the 
same  measure  point.  Thus,  if  the  line  be , which  is  parallel  to  ad, 
be  continued  to  meet  HPP,  and  an  isosceles  triangle  Qcku)  con 


311 


64 


PERSPECTIVE  DRAWING. 


structed  on  it,  as  indicated  by  the  dotted  lines  in  the  figure,  the 
base  ( uc ) of  this  isosceles  triangle  will  be  parallel  to  de,  and  its 
vanishing  point  will  be  coincident  with  vde. 

97.  There  is  a constant  relation  between  the  vanishing  point 
of  a system  of  lines  and  the  measure  point  for  that  system. 
Therefore,  if  the  vanishing  point  of  a system  of  lines  is  known, 
its  measure  point  may  be  found  without  reference  to  a diagram,  as 
will  be  explained. 

In  constructing  the  vanishing  points  vad  and  ved,fh  was  drawn 
parallel  to  ad,fg  was  drawn  parallel  to  ed,  and  since  hg  is  coinci- 
dent with  HPP,  the  two  triangles  ead  and  fhg  must  be  similar. 
As  ae  was  made  equal  to  ad  in  the  small  triangle,  hf  must  be  equal 
to  lig  in  the  large  triangle ; and  consequently  ved,  which  is  as  far 
from  vad  as  g is  from  h,  must  be  as  far  from  ^ad  as  the  point/ is 
from  the  point  h. 

If  the  student  will  refer  back  to  Figs.  8,  9,  and  9a,  he  will  see 
that  the  point  li  bears  a similar  relation  in  Fig.  26  to  that  of  the 
point  mH  in  Figs.  8,  9,  and  9a,  and  that  the  point  li  in  Fig.  26  is 
really  the  horizontal  projection  of  the  vanishing  point  vad.  (See 
also  § 32.)  Therefore,  as  ved  is  as  far  from  vad  as  the  point  h is 
from  the  point/,  we  may  make  the  following  statement,  which  will 
hold  for  all  systems  of  horizontal  lines. 

98.  The  measure  point  for  any  system  of  horizontal  lines  will  be 
found  on  VII  as  far  from  the  vanishing  point  of  the  system  as  the 
horizontal  projection  of  that  vanishing  point  is  distant  from  the  hori- 
zontal proj ection  of  the  station  point. 

Note.  — In  accordance  with  the  construction  shown  in  Fig. 
26,  SPV  will  always  lie  between  the  vanishing  point  of  a system 
and  its  measure  point. 

99.  The  measure  point  of  any  system  of  lines  is  usually  de- 
noted by  a small  letter  m with  an  index  corresponding  to  its  re- 
lated vanishing  point.  Thus,  mab  signifies  the  measure  point  for 
the  system  of  lines  vanishing  at  vah. 

100.  The  vanishing  point  for  ab  in  Fig.  26  has  been  found  at 
^ab.  The  point  n , in  HPP,  is  the  horizontal  projection  of  this 
vanishing  point.  The  measure  point  (mab)  for  all  lines  vanishing 
at  vah  will  be  found  on  VH,  at  a distance  from  vah  equal  to  the 
distance  from  n to  SPH  (98).  In  accordance  with  this  statement, 


312 


PERSPECTIVE  DRAWING. 


raab  has  been  found  by  drawing  an  arc  with  n as  center,  and  with 
a radius  equal  to  the  distance  from  n to  SI)ir,  and  dropping  from 
the  intersection  of  this  arc  with  IIPP  a vertical  line.  m&h  is 
found  at  the  intersection  of  this  vertical  line  with  VII. 

101.  The  perspective  of  ab  has  been  drawn  from  av,  vanishing 
at  vab.  avbl  on  VI^  is  made  equal  to  the  length  of  anb11  given 
in  the  plan  of  the  card.  A measure  line  through  vanishing  at 
mab,  will  determine  the  length  of  a?bv.  A line  from  bv  vanishing 
at  vad,  and  one  from  cF  vanishing  at  v*h,  will  intersect  at  <?p,  com- 
pleting the  perspective  plan  of  the  card. 

102.  Even  the  vanishing  points  (Vb  and  vad)  for  the  sides  of 
the  card  may  be  found  without  drawing  a diagram.  Since  fn  is 
drawn  parallel  to  ab , it  makes  the  same  angle  with  HPP  that  ab 
makes.  Similarly,  since  fh  is  drawn  parallel  to  ad , it  makes  the 
same  angle  with  HPP  that  ad  makes.  The  angle  between  fn  and 
fh  must  show  the  true  angle  made  by  the  two  lines  ab  and  ad  in 
the  diagram.  Therefore,  having  assumed  SPH,  we  have  sim- 
ply to  draw  two  lines  through  SPH,  making  with  HPP  the  respec- 
tive angles  that  the  two  sides  of  the  cards  are  to  make  with  the 
picture  plane,  care  being  taken  that  the  angle  these  two  lines 
make  with  one  another  shall  equal  the  angle  shown  between  the 
two  sides  of  the  card  in  the  given  plan.  Thus,  in  Fig.  27,  the 
two  projections  of  the  station  point  have  first  been  assumed.  Then 
through  SPH,  two  lines  (fn  and /A)  have  been  drawn,  making  re- 
spectively, with  HPP,  the  angles  (H°  and  N°)  which  it  is  desired 
the  sides  of  the  card  shall  make  with  the  picture  plane,  care  being 
taken  to  make  the  angle  between  fn  and  fh  equal  to  a right  angle, 
since  the  card  shown  in  the  given  plan  is  rectangular. 

Verticals  dropped  to  VH  from  the  points  n and  h will  deter- 
mine vab  and  vad.  Having  found  vab  and  vad,  mab  and  mad  should 
next  be  determined,  as  explained  in  § 98.  VHX  should  now  be 
assumed,  and  av  chosen  at  any  point  on  this  line.  It  is.  well  not 
to  assume  a?  very  far  to  the  right  or  left  of  an  imaginary  vertical 
line  through  SPV. 

From  av  the  sides  of  the  card  will  vanish  at  vab  and  vad  re- 
spectively. Measure  off  from  av  on  VH„  to  the  right,  a distance 
(cFb()  equal  to  the  length  of  the  side  aHbH  shown  in  the  given 
plan.  A measure  line  through  bv  vanishing  at  mab,  will  deter- 


313 


PERSPECTIVE  DRAWING. 


50 


mine  the  length  of  a7b7.  Measure  off  from  a7  on  VH^  to  the 
left,  a distance  (a7d{)  equal  to  the  length  of  the  side  aHc£H  shown 
in  the  given  plan.  A measure  line  through  dx  vanishing  at  mad, 
will  determine  the  length  of  a7d7. 

From  b7  and  dF,  the  remaining  sides  of  the  card  vanish  to 
vad  and  vab  respectively,  determining  by  their  intersection  the 
point  c7. 

The  line  aHdH  in  plan  is  divided  by  points  £H,  sH , and  rH. 
To  divide  the  perspective  («pdp)  of  this  line  in  a similar  manner, 
lay  off  on  YHj  from  a7,  to  the  left,  the  divisions  tx,  s1?  and  r1?  as 
taken  from  the  given  plan.  Measure  lines  through  q,  slf  and 
r1?  vanishing  at  mad,  will  intersect  a7d7,  and  determine  t7,  sp, 
and  r7. 

108.  As  has  already  been  stated,  the  true  length  of  any  line 
is  always  measured  on  YHj,  and  from  the  true  length,  the  length 
of  the  perspective  projection  of  the  line  is  determined  by  measure* 
lines  vanishing  at  the  measure  point  for  the  line  whose  perspective 
is  being1  determined.  Care  must  be  taken  to  measure  off  the  true 
length  of  the  line  in  the  proper  direction.  The  general  rule  for 
doing  this  is  as  follows  : — 

if  the  measure  point  of  any  line  is  at  the  right  of  SPV,  the 
true  length  of  the  line  will  be  laid  off  on  VH1  in  such  a man= 
ner  that  measurements  for  the  more  distant  points  in  the 
line  will  be  to  the  left  of  the  measurements  for  the  nearer 
points. 

Thus,  mad  is  at  the  right  of  SPV  The  point  d7  is  more  dis- 
tant than  the  point  t7.  Therefore,  the  measurement  (c?x)  for  the 
point  d7  will  be  to  the  left  of  the  measurement  for  the  point  tp . 
In  other  words,  since  mad  is  to  the  right  of  SPV,  dY,  which  repre- 
sents a point  more  distant  than  tv  must  be  to  the  left  of  tx,  the 
distance  between  tx  and  dY  being  equal  to  the  true  length  of  t7d7,  as 
shown  by  tKdH  in  the  given  plan. 

On  the  other  hand,  if  the  measure  point  for  any  system  of 
lines  is  to  the  left  of  SPV , the  true  measurements  for  any  line 
of  the  system  should  be  laid  off  on  VH1  in  such  a manner  that 
measurements  for  more  distant  points  on  the  line  are  to  the 
right  of  measurements  for  the  nearer  points  of  the  line. 


314 


PERSPECTIVE  DRAWING. 


57 


Thus,  raab  is  to  the  left  of  SPV.  The  point  bv  is  more  distant 
than  the  point  aF.  Therefore,  which  shows  the  true  measure- 
ment for  the  point  6P,  must  be  laid  off  to  the  right  of  av. 

104.  It  sometimes  happens  that  a line  extends  in  front  of 
the  picture  plane,  as  has  already  been  seen  in  the  lines  of  the 
nearest  corner  of  the  porch  in  Fig.  22.  It  may  be  desired  to 
extend  the  line  avdF  in  Fig.  27,  in  front  of  the  picture  plane,  to 
the  point  yF,  as  indicated  in  the  perspective  projection.  In  this 
case,  the  point  a p being  more  distant  than  the  point  yF,  and  w<ad 
being  to  the  right  of  SPV,  the  true  measurement  of  aFyF  must  be 
laid  off  on  YH,  in  such  a manner  that  the  measurement  for  aF 
will  be  to  the  left  of  the  measurement  for  yT.  In  other  words, 
yx  must  be  on  YH,  to  the  right  of  ap,  the  distance  aFyx  showing 
the  true  length  of  aFyF. 

Note.  — The  true  length  of  any  line  which  extends  in  front 
of  the  picture  plane  will  be  shorter  than  the  perspective  of  the 
line. 

105.  Having  determined  the  perspective  of  any  line,  as* 
dT c,p,  its  true  length  may  be  determined  by  drawing  measure  lines 
through  dF  and  cF.  The  distance  intercepted  on  YH,  by  these 
measure  lines  will  show  the  true  length  of  the  line.  Thus,  dFcv 
vanishes  at  vab.  Its  measure  point  must  therefore  be  mab.  Two 
lines  drawn  from  mab,  and  passing  through  cF  and  <F  respectively, 
will  intersect  YH,  in  the  points  cx  and  d2.  The  distance  between 
cx  and  d2  is  the  true  length  of  cTdT.  This  distance  will  be  found 
equal  to  aTbx,  which  is  the  true  measure  for  the  opposite  and 
equal  side  (ap6p)  of  the  rectangle. 

In  a similar  manner,  the  true  length  of  bFcF  may  be  found 
by  drawing  measure  lines  from  mad  through  bv  and  cv  respec- 
tively. b2c.}  will  show  the  true  length  of  <?bF,  and  should  be 
equal  to  aFdv  which  is  the  true  length  of  the  opposite  and  equal 
side  (ap<7p)  of  the  rectangle. 

106.  The  perspective  (wp)  of  a point  on  one  of  the  rear 
edges  of  the  card  may  be  determined  in  either  of  the  following 
ways : — 

1st.  From  b.„  which  is  the  intersection  Avith  YH,  of  the 
measure  line  through  6P,  lay  off  on  YH,,  to  the  left  (§103),  the 
distance  b2w2  equal  to  the  buwH  taken  from  the  given  plan.  A 


315 


58 


PERSPECTIVE  DRAWING. 


measure  line  through  w2,  vanishing  at  mad,  will  intersect  cTbv  at 
the  point  wv. 

2d.  In  the  given  plan  draw  a line  through  ?#H,  parallel  to  aH6H, 
intersecting  andn  in  the  point  w±.  On  VHX  make  apwl  equal  to 
allw^  as  given  in  the  plan.  A measure  line  through  vanish- 
ing at  mad,  will  determine  wz  on  avdv.  From  w3,  a line  parallel 
to  avhv  (vanishing  at  vab)  will  deterndne,  by  its  intersection  with 
bvev,  the  position  of  wv. 

107.  In  making  a perspective  by  the  method  of  perspective 
plan,  it  is  generally  customary  to  assume  Y1I  and  HPP  co- 
incident. That  is  to  say,  the  coordinate  planes  are  supposed  to 
be  in  the  position  shown  in  Fig.  9,  instead  of  being  drawn  apart 
as  indicated  in  Fig.  9a.  This, arrangement  simplifies  the  construc- 
tion somewhat. 

This  is  illustrated  in  Fig.  28,  which  shows  a complete  prob- 
lem in  the  method  of  perspective  'plan.  Compare  this  figure 
with  Fig.  27,  supposing  that,  in  Fig.  27,  HPP  with  all  its  related 
horizontal  projections  could  be  moved  downward,  until  it  just 
coincides  with  VH.  The  point  n would  coincide  with  vab,  h with 
vad,  and  the  arrangement  would  be  similar  to  that  shown  in  Fig. 
28.  All  the  principles  involved  in  the  construction  of  the  meas- 
ures, points,  etc.,  would  remain  unchanged. 

108.  The  vanishing  points  in  Fig.  28  have  first  been 
assumed,  as  indicated  at  yab  and  vad.  As  the  plan  of  the  object 
is  rectangular,  SPH  may  be  assumed  at  any  point  on  a semicircle 
constructed  with  valVd  as  diameter.  By  assuming  SPH  in  this 
manner,  lines  drawn  from  it  to  vab  and  vad  respectively  must  be 
at  right  angles  to  one  another,  since  any  angle  that  is  just  con- 
tained in  a semicircle  must  be  a right  angle.  These  lines  show 
by  the  angles  they  make  with  HPP,  the  angles  that  the  vertical 
walls  of  the  object  in  perspective  projection  will  make  with  the 
picture  plane  (§  102). 

109.  mad  and  mab  have  been  found,  as  explained  in  §97,  in 
accordance  with  the  rule  given  in  § 98. 

VH2  should  next  be  assumed  at  some  distance  below  VH,  to 
represent  the  vertical  trace  of  the  horizontal  plane  on  which  the 
perspective  plan  is  to  be  made  (§  91). 

The  position  of  av  (on  VH2)  may  now  be  assumed,  and  the 


316 


HPP 


Fig.  28 


\VHg 


PERSPECTIVE  DRAWING. 


59 


perspective  plan  of  the  object  constructed  from  the  given  plan, 
exactly  as  was  done  in  the  case  of  the  rectangular  card  in 
Fig.  27. 

110.  Having  constructed  the  complete  perspective  plan, 
every  point  in  the  perspective  projection  of  the  object  will  be 
found  vertically  above  the  corresponding  point  in  the  perspective 

plan. 

VHj  is  the  vertical  trace  of  the  plane  on  which  the  perspec- 
tive projection  is  supposed  to  rest.  a*  is  found  on  VHj  verti- 
cally over  aF  in  the  perspective  plan,  afef  is  a vertical  line  of 
measures  for  the  object,  and  shows  the  true  height  given  by  the 
elevation. 

To  find  the  height  of  the  apex  (^!P)  of  the  roof,  imagine  a 
horizontal  line  parallel  to  the  line  ah  to  pass  through  the  apex, 
and  to  be  extended  till  it  intersects  the  picture  plane.  A line 
drawn  through  &p,  vanishing  at  vab,  will  represent  the  perspective 
plan  of  this  line,  and  will  intersect  VH2  in  the  point  m,  which  is 
the  perspective  plan  of  the  point  where  the  horizontal  line 
through  tie  apex  intersects  the  picture  plane.  The  vertical  dis- 
tance laid  off  from  VH1?  will  show  the  true  height  of  the 

point  k above  the  ground,  kF  will  be  found  vertically  above 
kv , and  on  the  line  through  nl  vanishing  at  vab.  The  student  should 
find  no  difficulty  in  following  the  construction  for  the  remainder 
of  the  figure. 

111.  Fig.  29  illustrates  another  example  of  a similar  nature 
to  that  in  Fig.  28.  The  student  should  follow  carefully  through 
the  construction  of  each  point  and  line  in  the  perspective  plan 
and  in  the  perspective  projection.  The  problem  offers  no  especial 
difficulty. 

Plate  VI.  should  now  be  solved. 


CURVES. 

112.  Perspective  is  essentially  a science  of  straight  lines. 
If  curved  lines  occur  in  a problem,  the  simplest  way  to  find  their 
perspective  is  to  refer  the  curves  to  straight  lines. 

If  the  Curve  is  of  simple,  regular  form,  such  as  a circle  or  an 
ellipse,  it  may  be  enclosed  in  a rectangle.  The  perspective  of  the 


319 


60 


PERSPECTIVE  DRAWING. 


enclosing  rectangle  may  then  be  fonncl.  A curve  inscribed  within 
this  perspective  rectangle  will  be  the  perspective  of  the  given  curve. 

Fig.  30  shows  a circle  inscribed  in  a square.  The  points  of 
intersection  of  the  diameters  with  the  sides  of  the  square  give 

the  four  points  of  tangency  between  the 
square  and  circle.  The  sides  of  the 
square  give  the  directions  of  the  circle 
at  these  points.  Additional  points  on  the 
circle  may  be  established  by  drawing  the 
diagonals  of  the  square,  and  through 
the  points  mH,  &H,  wH,  and  W drawing 
construction  lines  parallel  to  the  sides 
of  the  square,  as  indicated  in  the  figureo 
Fig.  31  shows  the  square,  which  is 
supposed  to  lie  in  a horizontal  plane,  in 
parallel  perspective.  One  side  of  the 
square  (apc?p)  lies  in  the  picture  plane,  and  will  show  in  its  true 
size.  The  vanishing  point  for  the  sides  perpendicular  to  the 
picture  plane  will  coincide  with  SPV  (§  52,  note).  The  measure 
point  for  these  sides  has  been  found  at  mab,  in  accordance  with 


Fig. 30 


principles  already  explained.  avbl  is  laid  off  on  VH)  to  the  right 
of  the  point  ap,  equal  to  the  true  length  of  the  side  of  the  square. 
A measure  line  through  bY,  vanishing  at  mab,  will  determine  the 
position  of  the  point  6P.  bpcv  will  be  parallel  to  apdp  (§  54, 
note). 


320 


Plan 


PERSPECTIVE  DRAWING. 


61 


Fig.3Z 


The  diagonals  of  the  square  may  be  drawn.  Their  intersec- 
tion will  determine  the  perspective  center  of  the  square.  The 
diameters  will  pass  through  this  perspective  center,  one  vanishing 
at  SPV,  and  the  other  being  parallel  to  avdv 
(§  54,  note). 

Tbe  divisions  dFeF  and  aFfF  will  show 
in  their  true  size.  Lines  through  eF  and/1", 
vanishing  at  SPV,  will  intersect  the  diagonals 
of  the  square,  giving  four  points  on  the  per- 
spective of  the  circle.  Four  other  points  on 
the  perspective  of  the  circle  will  be  deter- 
mined by  the  intersections  of  the  diameter 
with  the  sides  of  the  square.  The  perspec- 
tive of  the  curve  can  be  drawn  as  indicated. 

113.  If  the  curve  is  of  very  irregular 
form,  such  as  that  shown  in  Fig.  32,  it  can 


be  enclosed  in  a rectangle,  and  the  rectangle  divided  by  lines, 
drawn  parallel  to  its  sides,  into  smaller  rectangles,  as  indicated  in 
the  figure. 

The  perspective  of  the  rectangle  with  its  dividing  lines  may 
then  be  found,  and  the  perspective  of  the  curve  drawn  in  free 


mab  HPPandVH  SP" 


hand.  This  is  shown  in  Fig.  33.  If  very  great  accuracy  is  re- 
quired, the  perspectives  of  the  exact  points  where  the  curve  crosses 
the  dividing  lines  of  the  rectangle  may  be  found. 


323 


62 


PERSPECTIVE  DRAWING. 


APPARENT  DISTORTION. 

114.  There  seems  to  exist  in  the  minds  of  some  beginners  in 
the  study  of  perspective,  the  idea  that  the  drawing  of  an  object 
made  in  accordance  with  geometrical  rules  may  differ  essentially 
from  the  appearance  of  the  object  in  nature.  Such  an  idea  is 
erroneous,  however.  The  only  difference  between  the  appearance 
of  a view  in  nature  and  its  correctly  constructed  perspective  pro- 
jection is  that  the  view  in  nature  may  be  looked  at  from  any  point , 
while  its  perspective  representation  shows  the  view  as  seen  from 
one  particular  point,  and  from  that  point  only. 

For  every  new  position  that  the  observer  takes,  he  will  see 
a new  view  of  the  object  in  space,  his  eye  always  being  at  the  apex 
of  the  cone  of  visual  rays  that  projects  the  view  he  sees  (see  Fig. 
1).  hi  looking  at  an  object  in  space,  the  observer  may  change  his 
position  as  often  as  he  likes,  and  will  see  a new  view  of  the  object 
for  every  new  position  that  he  takes. 

115.  This  is  not  true  of  the  perspective  projection  of  the 
object,  however.  Before  making  a perspective  drawing,  the  posi- 
tion of  the  observer’s  eye,  or  station  point,  must  be  decided  upon, 
and  the  resulting  perspective  projection  will  represent  the  object 
as  seen  from  this  point,  and  from  this  point  only.  The  observer, 
when  looking  at  the  drawing,  in  order  that  it  may  correctly  repre- 
sent to  him  the  object  in  space,  must  place  his  eye  exactly  at  the 
assumed  position  of  the  station  point.  If  the  eye  is  not  placed 
exactly  at  the  station  point,  the  drawing  will  not  appear  abso- 
lutely correct,  and  under  some  conditions  will  appear  much  dis- 
torted or  exaggerated. 

116.  Just  here  lies  the  defect  in  the  science  of  perspective.  It 
is  the  assumption  that  the  observer  has  but  one  eye.  Practically, 
of  course,  this  is  seldom  the  case.  A drawing  is  generally  seen 
with  two  eyes,  and  the  casual  observer  ne-ver  thinks  of  placing  his 
eye  in  the  proper  position.  Even  were  he  inclined  to  do  so,  it 
would  generally  be  beyond  his  power,  as  the  position  of  the  station 
point  is  seldom  shown  on  the  finished  drawing. 

117.  As  an  illustration  of  apparent  distortion,  consider  the 
perspective  projection  shown  in  Fig.  23.  In  order  that  the  per- 
spectives of  the  vanishing  points  might  fall  within  the  rather 


324 


PERSPECTIVE  DRAWING. 


G3 


narrow  limits  of  the  plate,  the  station  point  in  the  figure  has  been 
assumed  very  close  to  the  picture  plane,  the  distance  from  IIPP 
to  SI3H  showing  the  assumed  distance  from  the  paper  at  which 
the  observer  should  place  his  eye  in  order  to  obtain  a correct  view 
of  the  perspective  projection.  This  distance  is  so  short  it  is  most 
improbable  that  the  observer  will  ordinarily  place  his  eye  in  the 
proper  position  when  viewing  the  drawing.  Consequently  the 
perspective  projection  appears  more  or  less  unnatural  or  dis- 
torted. But,  for  the  sake  of  experiment,  if  the  student  will  cut 
a small,  round  hole,  one  quarter  of  an  inch  in  diameter,  from  a 
piece  of  cardboard,  place  it  directly  in  front  of  SPV  and  at  a dis- 
tance from  the  paper  equal  to  the  distance  of  SPH  from  HPP,  and 
if  he  will  then  look  at  the  drawing  through  the  hole  in  the  card- 
board, closing  the  eye  he  is  not  using,  he  will  find  that  the  unpleas- 
ant appearance  of  the  perspective  projection  disappears. 

It  will  thus  be  seen  that  unless  the  observer’s  eye  is  in  the 
proper  position  while  viewing  a drawing,  the  perspective  projec- 
tion may  give  a very  unsatisfactory  representation  of  the  object  in 
space. 

118.  If  the  observer’s  eye  is  not  very  far  removed  from  the 
correct  position,  the  apparent  distortion  will  not  be  great,  and  in 
the  majority  of  cases  will  be  unnoticeable.  In  assuming  the  posi- 
tion for  the  station  point,  care  should  be  taken  to  choose  such  a 
position  that  the  observer  will  naturally  place  his  eyes  there  when 
viewing  the  drawing. 

119.  As  a person  naturally  holds  any  object  at  which  he  is 
looking  directly  in  front  of  his  eyes,  the  first  thought  in  assuming 
the  station  point  should  be  to  place  it  so  that  it  will  come  very 
nearly  in  the  center  of  the  perspective  projection. 

120.  Furthermore,  the  normal  eye  sees  an  object  most  dis- 
tinctly when  about  ten  inches  away.  As  one  will  seldom  place 
a drawing  nearer  to  his  eye  than  the  distance  of  distinct  vision,  a 
good  general  rule  is  to  make  the  minimum  distance  between  the 
station  point  and  the  picture  plane  about  ten  inches.  For  a small 
drawing,  ten  inches  will  be  about  right ; but,  as  the  drawing  in- 
creases in  size,  the  observer  naturally  holds  it  farther  and  farther 
from  him,  in  order  to  embrace  the  whole  without  having  to  turn 
his  eye  too  far  to  the  right  or  left. 


325 


04 


PERSPECTIVE  DRAWING. 


121.  Sometimes  a general  rule  is  given  to  make  the  distance 
of  the  station  point  equal  to  the  altitude  of  an  equilateral  tri- 
angle, having  the  extreme  dimensions  of  the  drawing  for  its  base, 
and  the  station  point  for  its  apex. 

122.  The  apparent  distortion  is  always  greater  when  the 
assumed  position  of  the  observer’s  eye  is  too  near  than  when  it  is 
too  far  away.  In  the  former  case,  objects  do  not  seem  to  diminish 
sufficiently  in  size  as  they  recede  from  the  eye.  On  the  other 
hand,  if  the  observer’s  eye  is  between  the  assumed  position  of  sta- 
tion point  and  the  picture  plane,  the  effect  is  to  make  the  objects 
diminish  in  size  somewhat  too  rapidly  as  they  recede  from  the  eye. 
This  effect  is  not  so  easily  appreciated  nor  so  disagreeable  as  the 
former.  Therefore  it  is  better  to  choose  the  position  of  the  station 
point  too  far  away,  rather  than  too  near. 

123.  Finally,  the  apparent  distortion  is  more  noticeable  in 
curved  than  in  straight  lines,  and  becomes  more  and  more  dis- 
agreeable as  the  curve  approaches  the  edge  of  the  drawing.  Thus, 
if  curved  lines  occur,  great  pains  should  be  taken  in  choosing  the 
station  point ; and,  if  possible,  such  a view  of  the  object  should  be 
shown  that  the  curves  will  fall  near  the  center  of  the  perspective. 

124.  The  student  should  realize  that  the  so-called  distortion 
in  a perspective  projection  is  only  an  apparent  condition.  If  the 
eye  of  the  observer  is  placed  exactly  at  the  position  assumed  foi 
it  when  making  the  drawing,  the  perspective  projection  will  exactly 
represent  to  him  the  corresponding  view  of  the  object  in  space. 


326 


EXAMINATION  PAPER 


PLATE  I 


PERSPECTIVE  DRAWING. 


Data  to  be  used  by  student  in  solving  plates.  Leave  all  necessary  con- 
struction lines.  Letter  all  points,  vanishing  points,  lines,  etc.,  as  found,  in 
accordance  with  the  notation  given  in  the  Instruction  Paper. 


spective  of  the  point  a.  Also  in  each  problem  locate  the  positions 
of  the  point  a,  and  of  the  station  point,  as  follow : — 


PROBLEMS  VII.  and  VIII.  Find  the  perspective  of  the 
line  A. 

PROBLEMS  IX.  and  X.  Find  the  perspective  of  the 
vanishing  point  of  the  system  of  lines  parallel  to  the  given 
line  A. 

PROBLEM  XI.  Find  from  the  given  plan  and  elevation 
the  perspective  projection  of  the  rectangular  block. 

The  view  to  be  shown  is  indicated  by  the  diagram.  The 
station  point  is  to  be  inches  in  front  of  the  picture  plane. 
The  position  of  SPV  is  given.  The  perspective  projection  is  to 
rest  upon  a horizontal  plane  2 inches  below  the  level  of  the  eye. 
Invisible  lines  in  the  perspective  projection  should  be  dotted. 


PLATE  I. 


PROBLEMS  I.,  II.,  III.,  IV.,  V.,  and  VI.  Find  the  per= 


the  plane  of  the  horizon., 


Station  point inches  in  front  of  the  picture  plane. 


67 


329 


68 


PERSPECTIVE  DRAWING. 


PLATE  II. 

PROBLEM  XII.  To  find  the  perspective  of  a cube  the 
sides  of  which  are  If  inches  long,  resting  on  a horizontal  plane 
i inch  below  the  observer’s  eye. 

The  nearest  edge  of  the  cube  is  about  IT  inches  behind  the 
picture  plane,  as  shown  by  the  relation  between  the  given  diagram 
and  HPP.  The  station  point  is  to  be  3|  inches  in  front  of  the 
picture  plane.  The  position  of  SPV  is  given.  Invisible  edges 
of  the  cube  should  be  dotted  in  the  perspective  projection. 

PROBLEM  XIII.  To  find  the  perspective  of  a cube  similar 
to  that  in  the  last  problem. 

The  position  of  the  cube  is  such  that  it  intersects  the  picture 
plane  as  indicated  by  the  relation  between  the  given  diagram 
and  HPP.  The  cube  is  supposed  to  rest  on  the  horizontal  plane 
represented  by  VHj.  The  station  point  is  to  be  3|  inches  in  front 
of  the  picture  plane.  The  position  of  SPV  is  given.  Invisible  edges 
should  be  dotted  in  the  perspective  projection. 

PROBLEM  XIV.  Block  pierced  by  a rectangular  hole. 

The  plan  and  elevation  given  in  the  figure  represent  a rectan- 
gular block  pierced  by  a rectangular  hole  which  runs  horizontally 
through  the  block  from  face  to  face,  as  indicated.  The  diagram, 
HPP,  and  the  position  of  SPV  are  given.  The  block  is  to  rest  on  a 
horizontal  plane  2|  inches  below  the  observer’s  eye.  The  observer’s 
eye  is  to  be  6|  inches  in  front  of  the  picture  plane.  Find  the  per- 
spective projection  of  the  block  and  of  the  rectangular  hole. 
All  invisible  lines  in  the  perspective  projection  should  be  dotted. 

PLATE  III. 

PROBLEM  XV.  Find  the  perspective  projection  of  the 
house  shown  in  plan,  side  and  end  elevations. 

The  diagram,  HPP,  and  the  projections  of  the  station  point 
are  given.  The  house  is  supposed  to  rest  on  a horizontal  plane 
lyA  inch  below  the  observer’s  eye.  Invisible  lines  in  this  per- 
spective projection  need  not  be  shown  except  as  they  may  be 
needed  for  construction.  All  necessary  construction  lines  should 
be  shown ; but  the  points  in  the  perspective  projection  need  not  be 
lettered,  except  ap,  6P,  ep , and  dF. 


330 


PLATE  II 


HPP 


VH 

"sp'3 


"sV 


Vh 


VH, 


%P« 


DATE 


NAME 


PERSPECTIVE  DRAWING. 


69 


PLATE  IV. 


PROBLEM  XVI. 

The  plate  shows  the  plan,  front,  and  side  elevations  of  a 
house.  In  order  to  assist  the  student  in  understanding  these 
drawings,  an  oblique  projection  (at  one-half  scale)  is  given,  with 
the  visible  lines  and  planes  lettered  to  agree  with  those  in  the 
plan  and  elevations. 

The  problem  is,  first,  to  find  a complete  Vanishing  Point 
Diagram  (§  75)  for  the  house  in  the  position  indicated  by  the 
given  diagram ; second,  to  draw  the  perspective  projection  of 
the  house,  resting  on  a horizontal  plane  six  inches  below  the  level 
of  the  observer’s  eye.  The  projections  of  the  station  point  ^are 
given. 

There  will  be,  including  the  vertical  system,  eleven  systems 
of  lines  aiid  eight  systems  of  planes  in  the  vanishing  point  dia- 
gram. 

Note.  — The  lines  of  these  systems  can  most  easily  he  iden- 
tified by  first  finding  their  horizontal  projections  on  the  plan. 

In  finding  the  vanishing  points  for  the  different  systems,  the 
student  should  proceed  in  the  following  order  : — 

1st.  Draw  VH  the  vanishing  trace  for  all  horizontal  planes. 

2d.  Find  vab,  the  vanishing'  point  for  all  horizontal  lines  in 
the  house  that  vanish  to  the  right. 

3d.  Find  vad,  the  vanishing  point  for  all  horizontal  lines  van- 
ishing to  the  left. 

4th.  Find  von.  The  line  on  forms  the  intersection  of  the 
planes  Nx  and  Uj  (see  oblique  projection).  To  this  same  system 
belong  the  lines  rq , ts , and  zy. 

5th.  Find  vum.  The  line  nm  forms  the  intersection  of  the 
planes  Mj  and  XJ)  (see  oblique  projection).  To  this  same  system 
belong  the  lines  qp,  vu , and  xw. 

6th.  Find  vfl.  The  line  ft  forms  the  intersection  of  the 
planes  S and  Vt.  The  line  jk  also  belongs  to  this  same  system. 

7th.  Find  rig.  The  line  Ig  forms  the  intersection  of  the 
planes  R and  Yv  The  line  kli  also  belongs  to  this  system. 


333 


70 


PERSPECTIVE  DRAWING. 


8th.  Find  vd;i.  The  line  dj  forms  the  intersection  of  the 
planes  P and  M.  To  this  same  system  belongs  the  line  which 
forms  the  intersection  of  the  planes  P and  Mj 

9th.  Find  vgb.  The  line  gb  forms  the  intersection,  of  the 
planes  N and  O.  To  this  same  system  belongs  the  line  which 
forms  the  intersection  between  the  planes  Nx  and  O. 

10th.  Draw  the  vanishing  traces  of  the  planes  M,  N,  O,  P, 
R,  S,  U,  and  V,  checking  the  construction  of  the  vanishing  points 
already  found. 

11th.  vaf  will  now  be  determined  by  the  intersection  of  TP 
and  TN  (§  74).  The  lines  forming  the  intersection  of  the  plane 
P with  the  planes  N and  Nx  will  vanish  at  vaf. 

In  a similar  manner  vhc  will  be  determined  by  the  intersection 
of  TM  and  TO.  The  lines  forming  the  intersections  of  the  plane 
O with  the  planes  M and  Mx  will  vanish  at  vhc. 

The  complete  vanishing  point  diagram  has  now  been  found ; 
and  it  remains  only  to  establish  VH^  in  accordance  with  the  given 
data,  and  construct  the  perspective  projection  of  the  house.  A 
bird’s-eye  view  has  been  chosen  for  the  perspective  projection  in 
order  to  show  as  many  of  the  roof  lines  as  possible. 

Each  visible  line  in  the  perspective-  projection  should  be  con- 
tinued by  a dotted  construction  line,  to  meet  its  particular  van- 
ishing point. 

This  problem  will  require  more  care  in  draughting  than  any 
of  the  previous  ones,  and  the  angles  of  the  lines  in  revolved  plan 
and  elevation  should  be  laid  off  with  great  precision.  The  stu- 
dent should  not  attempt  to  make  the  perspective  projection  until 
the  vanishing  point  diagram  is  drawn  with  accuracy. 

PLATE  V. 

PROBLEM  XVII. 

From  the  given  data  construct  a perspective  projection,  using 
the  plan  of  view  for  a diagram  as  indicated.  HPP,  VHl5  SPV, 
and  SPH  are  given. 

This  plate  need  not  be  lettered,  except  as  the  student  may 
find  it  an  aid  in  construction. 


334 


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Q 


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□ 

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> 


PERSPECTIVE  DRAWING, 


71 


PLATE  VI. 

PROBLEM  XVIII. 

Construct,  by  the  method  of  perspective  plan,  a perspective 
projection  of  the  object  shown  in  the  given  plan  and  elevations. 

HPP  and  VH  are  to  be  taken  coincident  (§  107),  as  in- 
dicated on  the  plate. 

The  vanishing  points  (vab  and  vad)  for  the  two  systems  of 
horizontal  lines  in  the  object  are  given.  The  line  ab  is  to  make 
an  angle  of  60°  with  the  picture  plane. 

VH2  is  the  vertical  trace  of  the  horizontal  plane  on  which 
the  perspective  plan  is  to  be  drawn.  The  corner  («p)  of  this  plan 
is  given.  The  perspective  projection  of  the  object  is  to  rest  on 
the  horizontal  plane  determined  by  VH!. 

An  oblique  projection  of  the  object  is  given  to  assist  in  read- 
ing the  plan  and  elevations. 

The  student  may  use  his  discretion  in  lettering  this  plate. 
No  letters  are  required  except  those  indicating  the  positions  of 
the  station  point  and  the  measure  points. 


337 


plate:  vi 


date: 


RENAISSANCE  CAPITA!.. 

An  example  of  charcoal  drawing. 


FREEHAND  DRAWING, 


1.  The  Value  cf  Freehand  Drawing  to  an  Architect.  Out- 
side of  its  general  educational  value  freehand  drawing  is  as  abso- 
lutely  essential  to  the  trained  architect  as  it  is  to  the  professional 
painter.  It  is  obviously  necessary  for  the  representation  of  all 
except  the  most  geometric  forms  of  ornament,  and  it  is  equally 
important  in  making  any  kind  of  a rapid  sketch,  either  of  a whole 
building  or  a detail,  whether  from  nature  or  in  the  study  of  plans 
and  elevations.  It  is  perhaps  not  so  generally  understood  that  the 
training  it  gives  in  seeing  and  recording  forms  accurately,  culti- 
vates not  only  the  feeling  for  relative  proportions  and  shapes,  but, 
also,  that  very  important  architectural  faculty — the  sense  of  the 
third  dimension.  The  essential  problem  of  most  drawing  is  to 
express  length,  breadth,  and  thickness  on  a surface  which  has 
only  length  and  breadth.  As  the  architect  works  out  on  paper, 
which  has  only  length  and  breadth,  his  designs  for  buildings  which 
are  to  have  length,  breadth,  and  thickness,  he  is  obliged  to  visual- 
ize;  to  see  with  the  mind’s  eye  the  thickness  of  his  forms.  lie 
must  always  keep  in  mind  what  the  actual  appearance  will  be. 
The  study  of  freehand  drawing  from  solid  forms  in  teaching  the 
representation  on  paper  of  their  appearance,  stimulates  in  the 
draughtsman  his  power  of  creating  a mental  vision  of  any  solid. 
That  is,  drawing  from  solids  educates  that  faculty  by  means  of 
which  an  architect  is  able  to  imagine,  before  it  is  erected,  the 
appearance  of  his  building. 

2.  Definition  of  Drawing.  A drawing  is  a statement  of  cer- 
tain facts  or  truths  by  means  of  lines  and  tones.  It  is  nothing 
more  or  less  than  an  explanation.  The  best  drawings  are  those  in 
which  the  statement  is  most  direct  and  simple;  those  in  which  the 
explanation  is  the  clearest  and  the  least  confused  by  the  introduc- 
tion of  irrelevant  details. 

A drawing  never  attempts  to  tell  all  the  facts  about  the  form 
depicted,  and  each  person  who  makes  a drawing  selects  not  only 
the  leading  truths,  but  also  includes  those  characteristics  which 


341 


0 


FREEHAND  DRAWING 


appeal  to  him  as  an  individual.  The  result  is  that  no  two  people 
make  drawings  of  the  same  subject  exactly  alike. 

3.  The  Eye  and  the  Camera.  The  question  immediately 
arises:  Why  should  we  not  draw  all  that  we  see;  tell  all  that  we 
know  about  our  subject  ? Since  the  photograph  does  represent, 
with  the  exception  of  color,  all  that  we  see  and  even  more,  another 
question  is  raised:  AVliat  is  the  essential  difference  between  a 

photograph  of  an  object  and  a drawing  of  an  object  ? These  are 
questions  which  bring  us  dangerously  near  the  endless  region  of 
the  philosophy  of  fine  arts.  Stated  simply  and  broadly,  art  is  a 
refuge  invented  by  man  as  an  escape  from  the  innumerable  and 
bewildering  details  of  nature  which  weary  the  eye  and  mind  when 
we  attempt  to  grasp  and  comprehend  them. 

Without  going  into  an  explanation  of  the  differences  in  struct- 
ure between  the  lens  of  a camera  and  the  lens  of  the  eye,  it  may 
be  accepted  as  a general  statement  that  in  spite  of  apparent  errors 
of  distortion  the  photograph  gives  us  an  exact  reproduction  of 
nature.  Every  minutest  detail,  every  shadow  of  a shade,  is  pre- 
sented as  being  of  equal  importance  and  interest,  and  it  is  easy  to 
demonstrate  that  the  camera  sees  much  more  detail  than  the  human 
eye.  In  any  good  photograph  of  an  interior  the  patterns  on  the 
walls  and  hangings,  the  carving  and  even  the  grain  and  texture  of 
woods  are  all  presented  with  equal  clearness.  In  order  to  perceive 
any  one  of  those  details  as  clearly  with  the  eye  it  would  be  neces- 
sary to  focus  the  eye  on  that  particular  point,  and  while  so  focused 
all  the  other  details  of  the  room  would  appear  blurred.  The  camera, 
on  the  contrary,  while  focused  at  one  point  sees  all  the  others  with 
almost  equal  clearness.  This  fact  alone  is  enough  to  demonstrate  tlie 
danger  of  assuming  that  the  photograph  is  true  to  the  facts  of  vision. 
Again,  a photograph  of  an  antique  statue  will  exaggerate  the  im- 
portance of  the  weather  stains  and  disfigurements  at  the  expense  of 
the  subtle  modelling  of  the  muscular  parts  which  the  eye  would 
instinctively  perceive  first. 

Nature,  then,  and  the  photograph  from  nature,  is  a bewilder- 
ing mass  of  detail.  The  artist  is  the  man  of  trained  perceptions 
who,  by  eliminating  superfluous  detail  and  grasping  and  present- 
ing only  the  essential  characteristics,  produces  a drawing  in  which 
we  see  the  object  in  a simplified  but  nevertheless  beautiful  form. 


342 


FREEHAND  DRAWING 


3 

In  looking  at  the  drawing  we  become  conscious  of  the  subject  and 
its  principal  attributes;  we  comprehend  and  realize  these  with  far 
less  effort  of  the  mind  and  eye  than  we  should  expend  in  taking 
in  and  comprehending  the  real  object  or  a photograph  of  it.  Com- 
pared to  nature  it  is  more  restful  and  more  easily  understood,  and 
the  ease  with  which  it  is  comprehended  constitutes,  the  psycholo- 
gists say,  a large  part  of  the  pleasure  we  take  in  art;  it  certainly 
explains  why  we  enjoy  a drawing  of  an.  object  when  we  may  take 
no  pleasure  in  the  object  itself,  or  a photograph  of  it. 

4.  Restraint  in  Drawing.  The  practical  application  of  the 
preceding  broad  definition  is  neither  difficult  nor  abstruse.  The 
beginner  in  drawing  usually  finds  his  work  swamped  in  a mass  of 
detail,  because  his  desire  is  to  be  absolutely  truthful  and  accurate, 
and  the  more  he  has  read  Ruskin*  and  writers  of  his  school  the 
more  does  he  feel  that  art  and  nature  are  one,  and  that  the  best 
drawing  is  that  which  most  successfully  reproduces  nature  with 
photographic  fidelity.  It  maybe  taken  for  granted  that  a drawing 
must  be  true;  true  to  nature.  But  truth  is  at  best  a relative 
term,  and  while  it  may  be  said  that  every  normal  eye  sees  prac- 
tically the  same,  yet,  after  all,  the  eye  sees  only  what  it  is  trained 
to  see.  It  is  the  purpose  of  all  teaching  of  drawing  to  train  the 
eye  to  see  and  the  hand  to  put  down  the  biggest  and  most  impor- 
tant truths  and  to  sacrifice  small  and  unimportant  details  for  the 
sake  of  giving  greater  emphasis  or  accent  to  the  statement  of  the 
larger  ones.  “Art  lives  by  sacrifices”  is  the  expression  of  the 
French,  the  most  artistic  nation  of  modern  times.  The  experience 
of  the  beginner  is  very  practical  testimony  to  the  truth  of  the 
expression,  for  he  very  soon  realizes  that  he  lias  not  the  ability, 
even  if  it  were  best,  to  draw  all  he  sees,  and  he  has  to  face  the 
question  of  what  to  leave  out,  what  to  sacrifice.  Sense  will  tell 
him  that  he  must  at  all  costs  retain  those  elements  which  have  the 
most  meaning  or  significance,  or  else  his  drawing  will  not  be  in- 
telligible.  So  he  is  gradually  taught  to  select  the  vital  facta  and 
make  sure  of  them  at  least.  It  is  true  that  the  more  accomplished 
the  draughtsman  becomes  the  greater  will  be  his  ability  to  suc- 
cessfully represent  the  lesser  truths,  the  smaller  details  he  sees, 

* Note.— Ample  corroboration  for  all  that  is  stated  above  may  be  found  in  Ruskin, 
but  it  is  embedded  in  a mass  of  confusing  and  contradictory  assertions.  Ruskin  is  a very 
dangerous  author  for  the  beginner. 


343 


4 


FREEHAND  DRAWING 


because  having  trained  his  perception  to  the  importance  of  grasping 
the  big  truths  he  has  also  attained  the  knowledge  and  ability  to 
express  the  smaller  facts  without  obscuring  the  greater  ones. 
Nevertheless  the  question  of  what  to  sacrifice  remains  one  of  the 
most  important  in  all  forms  of  representation.  One  of  the  com- 
monest criticisms  pronounced  by  artists  on  the  work  of  their  col- 
leagues is  that  “ he  has  not  known  when  to  stop”;  the  picture  is 
overloaded  and  obscured  with  distracting  detail. 

5.  Learning  to  See.  It  is  very  important  that  the  student 
of  drawing  shall  understand  in  the  beginning  that  a very  large  part 
of  his  education  consists  in  learning  to  see  correctly.  The  power 
to  see  correctly  and  the  manual  skill  to  put  down  with  accuracy 
what  he  sees — these  he  must  acquire  simultaneously.  It  is  usually 
difficult  at  first  to  convince  people  that  they  do  not  naturally  and 
without  training  see  correctly.  It  is  true  that  there  is  formed 
in  every  normal  eye  the  same  image  of  an  object  if  it  is  seen  from 
the  same  position,  but  as  minds  differ  in  capacity  and  training, 
so  will  they  perceive  differently  whatever  is  thrown  upon  the  retiqa 
or  mirror  of  the  eye. 

It  is  a matter  of  common  observation  that  no  two  people  agree 
in  their  description  of  an  object,  and  where  events  are  taking  place 
rapidly  in  front  of  the  eyes,  as  in  a football  game,  one  person  with 
what  we  call  quick  perceptions,  will  see  much  more  than  another 
whose  mind  works  more  slowly;  yet  the  same  images  were  formed 
in  the  eyes  of  each.  The  person  who  understands  the  game  sees 
infinitely  more  of  its  workings  than  one  who  does  not,  because 
he  knows  what  to  look  for;  and  to  draw  with  skill  one  must  also 
know  what  to  look  for.  Many  people  who  have  not  studied  draw- 
ing say  they  see  the  top  of  a circular  table  as  a perfect  circle  in 
whatever  position  the  eye  may  be  in  regard  to  the  table.  Others 
see  a white  water  lily  as  pure  white  in  color,  whether  it  is  in  the 
subdued  light  of  an  interior  or  in  full  sunlight  out  of  doors.  I11 
questions  of  color  it  is  a matter  of  much  study,  even  with  persons 
of  artistic  gifts  and  training,  to  see  that  objects  of  one  color  appear 
under  certain  conditions  to  be  quite  a different  color. 

6.  OutSineo  The  untrained  eye  usually  sees  objects  in  out- 
line filled  in  with  their  local  color,  that  is,  the  color  they  appear  to 
be  when  examined  near  the  eye  without  strong  light  or  shade 


344 


FREEHAND  DRAWING 


5 


thrown  upon  them.  One  of  the  first  things  the  student  has  to 
learn  is  that  there  are  no  outlines  in  nature.  Objects  are  distin- 
guished from  each  other  not  by  outlines  but  by  planes  of  light  and 
dark  and  color.  Occasionally  a plane  of  dark  will  be  so  narrow 
that  it  can  only  be  represented  by  a line,  but  that  does  not  refute 
the  statement  that  outlines  do  not  exist  in  nature.  Very  often 
only  one  part  of  an  object  will  be  detached  from  its  surroundings. 
Some  of  its  masses  of  light  may  fuse  with  the  light  parts  of  other 
forms  or  its  shadows  with  surrounding  shadows.  If  enough  of  the 
form  is  revealed  to  identify  it,  the  eye  unconsciously  supplies  the 
shapes  which  are  not  seen,  and  is  satisfied.  The  beginner  in 
drawing  is  usually  not  satisfied  to  represent  it  so,  but  draws 
definitely  forms  which  he  does  not  see  simply  because  he  knows 
they  are  there.  Obviously  then  it  is  necessary  to  learn  what  we 
do  not  see  as  well  as  what  we  do. 

7.  Although  there  are  no  outlines  in  nature,  most  planes  of 
light  and  shade  have  definite  shapes  which  serve  to  explain  the 

•form  of  objects  and  these  shapes  all  have  contours,  edges  or  bound- 
aries where  one  tone  stops  and  another  begins.  As  the  history  of 
drawing  shows,  it  has  always  been  a convention  of  early  and  primi- 
tive races  to  represent  these  contours  of  objects  by  lines,  omitting 
effects  of  iight  and  shade.  To  most  people  to-day  the  outline  of 
an  object  is  its  most  important  element — that  by  which  it  is  most 
easily  identified — and  for  a large  class  of  explanatory  drawings 
outlines  without  light  and  shade  are  sufficient.  By  varying  the 
width  and  the  tone  of  the  outline  it  is  even  possible  to  suggest  the 
solidity  of  forms  and  something  of  the  play  of  light  and  shade  and 
of  texture. 

8.  Since,  in  order  to  represent  light  and  shade,  it  is  neces- 
sary to  set  off  definite  boundaries  or  areas  and  give  them  their 
proper  size  and  contour,  it  follows  that  the  study  of  outline  may 
very  well  be  considered  a simple  way  of  learning  to  draw,  and  a 
drawing  in  outline  as  one  step  in  the  production  of  the  fully  devel- 
oped work  in  light  and  shade.  An  outline  drawing  is  the  simplest 
one  which  can  be  made,  and  by  eliminating  all  questions  of  light 
and  shade  the  student  can  concentrate  all  his  effort  on  representing 
contours  and  proportions  correctly.  But  he  should  always  bear  in 
mind  that  his  drawing  is  a convention,  that  it  is  not  as  he  actually 


345 


6 


FREEHAND  DRAWING 


sees  nature,  and  that  it  can  but  imperfectly  convey  impressions  of 
the  surfaces,  quality  and  textures  of  objects. 

9.  It  is  often  asserted  that  whoever  can  learn  to  write  can 
learn  to  draw,  but  one  may  go  further  and  assert  that  writing  is 
drawing.  Every  letter  in  a written  word  is  a drawing  from  mem- 
ory of  that  letter.  So  that  it  may  be  assumed  that  every  one  who 
can  write  already  knows  something  of  drawing  in  outline,  which 
is  one  reason  why  instruction  in  drawing  may  logically  begin 
with  the  study  of  outline. 

Some  good  teachers  advocate  the  immediate  study  of  light 
and  shade,  arguing  that  since  objects  in  nature  are  not  bounded  by 
lines  to  represent  them  so  it  is  not  only  false  but  teaches  the 
student  to  see  in  lines  instead  of  thinking  of  the  solidity  of  objects. 
But  these  arguments  are  not  sufficient  to  overbalance  those  in 
favor  of  beginning  with  outline,  especially  in  a course  planned  for 
architectural  students  to  whom  expression  in  outline  is  of  the  first 
importance. 

nATERIALS. 

10.  Pencils.  Drawings  may  be  made  in  “ black  and  white” 
or  in  color.  A black  and  white  drawing  is  one  in  which  there  is 
no  color  and  is  made  by  using  pencil,  charcoal,  crayon  or  paint 
which  produces  different  tones  of  gray  ranging  from  black  to  white. 

The  pencil  is  the  natural  medium  of  the  architect  and  the 
materials  for  pencil  drawing  are  very  inexpensive  and  require  little 
time  for  their  preparation  and  care.  Drawings  in  pencil  are  very 
easily  changed  and  corrected  if  necessary.  All  the  required  plates 
for  this  course  are  to  be  executed  in  pencil. 

The  pencil  will  make  a drawing  with  any  degree  of  finish 
ranging  from  a rough  outline  sketch  to  the  representation  of  all 
the  light  and  shade  of  a complicated  subject.  In  addition  it  is  the 
easiest  of  all  mediums  to  handle.  Students  are  sometimes  led  to 
think  that  it  is  more  artistic  to  draw  in  charcoal  crayon  or  pen 
and  ink.  It  may  be  that  an  additional  interest  is  aroused  in  some 
students  by  working  in  these  materials,  but  the  beginner  must 
assure  himself  at  once  that  artistic  merit  lies  wholly  in  the  result 
and  not  at  all  in  the  material  in  which  the  work  is  executed. 

Pencils  are  made  in  varying  degrees  of  hardness.  The  softest 


346 


FREEHAND  DRAWING 


7 


is  marked  BBBBBB  or  OB;  5B  is  slightly  less  soft  and  they  increase 
in- hardness  through  the  following  grades:  4B,  3B,  2B,  B,  IIB,  F, 
H,  211,  311,  411,  5 II,  OH.  A pencil  should  mark  smoothly  and 
be  entirely  free  from  grit.  The  presence  of  grit  is  easily  recog- 
nized by  the  scratching  of  the  pencil  on  the  paper  and  by  the 
unevenness  in  the  width  and  tone  of  the  line.  The  leads  of  the 
softer  pencils  are  the  weaker  and  are  more  easily  broken.  They 
give  off  their  color  the  most  freely  and  produce  blackest  lines. 
What  hardness  of  pencils  one  should  use  depends  upon  a number 
of  considerations,  one  of  the  most  important  being  the  quality  of 
paper  upon  which  the  drawing  is  made. 

Quick  effects  of  light  and  shade  can  be  best  produced  by  the 
use  of  soft  pencils  because  they  give  off  the  color  so  freely  and  the 
strokes  blend  so  easily  into  flat  tones. 

A medium  or  hard  pencil  is  necessary  when  a drawing  is  to 
be  small  in  size  and  is  intended  to  express  details  of  form  and  con- 
struction rather  than  masses  of  light  and  shade.  This  is  because 

o 

the  lines  made  by  hard  pencils  are  liner,  and  more  clean  and  crisp 
than  can  be  obtained  by  using  soft  grades.  The  smaller  the  draw- 
ing, the  more  expression  of  detail  desired,  the  harder  the  pencil 
should  be;  a good  general  rule  for  all  quick  studies  of  effects  of 
light  and  shade  is  to  use  as  soft  a pencil  as  is  consistent  with  the 
size  of  the  drawing  and  the  surface  of  the  paper.  Beginners,  how- 
ever, are  obliged  to  make  many  trial  lines  to  obtain  correct  propor- 
tions, and  in  that  way  produce  construction  lines  so  heavy  that 
the  eraser  required  to  remove  them  leaves  the  paper  in  a damaged 
condition.  Until  the  student  can  draw  fairly  well  he  should  begin 
every  piece  of  work  with  a medium  pencil  and  take  care  to  make 
very  light  lines  and  especially  to  avoid  indenting  the  paper. 

It  should  be  understood  that  pencil  drawings  ought  never  to 
be  very  large.  There  should  always  be  a proportional  relation 
between  the  size  of  a drawing  and  the  medium  which  produces  it. 
The  point  of  a pencil  is  so  small  that  to  make  a large  drawing 
with  it  consumes  a disproportionate  amount  of  time.  For  large 
drawings,  especially  such  showing  light  and  shade,  crayon  or  char- 
coal are  the  proper  materials  for  they  can  be  made  to  cover  a large 
surface  in  a very  short  time.  The  larger  the  area  to  be  covered 
the  larger  should  be  the  point  and  the  line  producing  it. 


347 


8 


FREEHAND  DRAWING 


Special  pencils  with  large  leads  can  be  obtained  for  making 
large  pencil  drawings. 

11.  Paper.  In  general  the  firmer  the  surface  of  the  paper 
the  harder  the  pencil  one  can  use  on  it.  For  a medium  or  hard 
pencil  the  paper  should  be  tough  and  rather  smooth  but  never 
glazed.  Many  very  cheap  grades  of  paper,  for  example  that  on 
which  newspapers  are  printed,  take  the  pencil  very  well  but  have 
not  a sufficiently  tough  surface  to  allow  the  use  of  the  eraser.  They 
are  excellent  for  rapid  sketches  made  very  directly  without  altera- 
tions. 

Paper  for  effects  of  light  and  shade  should  be  soft  and  smooth. 
For  this  work  the  cheaper  grades  of  paper  are  often  more  suitable 
than  the  expensive  sorts.  Paper  with  a rough  surface  should 
always  be  avoided  in  pencil  drawings,  as  it  gives  a disagreeable 
“ wooly  ” texture  to  the  lines. 

12.  Holding  the  Pencil.  Any  hard  and  fast  rules  for  the 
proper  use  of  the  pencil  would  be  out  of  place,  but  until  the  stu- 
dent has  worked  out  for  himself  the  ways  which  are  the  easiest  and 
best  for  him  he  cannot  do  better  than  adoot  the  following;  sugges- 
tions,  which  will  certainly  aid  him  in  using  the  pencil  with  effect 
and  dexterity. 

The  most  important  points  in  drawing  are  to  be  accurate  and 
at  the  same  time  direct  and  free.  Of  course,  accuracy — the  ability 
to  set  down  things  in  their  right  proportions — is  indispensable; 
but  the  abilty  to  do  this  in  the  most  straightforward  way  without 
constraint,  fumbling,  and  erasures  is  also  necessary.  Art  has  been 
defined  as  the  doing  of  any  one  thing  supremely  well. 

The  pencil  should  be  held  lightly  between  the  thumb  and 
forefinger  three  or  four  inches  from  the  point,  supported  by  the 
middle  finger,  with  hand  turned  somewhat  on  its  side. 

There  are  three  ways  in  which  it  is  possible  to  move  the  pen- 
cil; with  the  fingers,  the  wrist,  or  the  arm.  Most  people  find  it 
convenient  to  use  the  finger  movement  for  drawing  short,  vertical 
lines.  In  order  to  produce  a long  line  by  this  movement  it  is  only 
necessary  to  make  a succession  of  short  lines  with  the  ends  touch- 
ing each  other  but  not  overlapping,  or  by  leaving  the  smallest  pos- 
sible space  between  the  end  of  one  line  and  the  beginning  of  the 
next.  The  wrist  movement  produces  a longer  line  and  is  used 


348 


FREEHAND  DRAWING 


9 


naturally  to  make  horizontal  lines.  For  a very  long  sweep  of  line 
the  movement  of  the  arm  from  the  shoulder  is  necessary.  This  is, 
perhaps,  the  most  difficult  way  of  drawing  for  the  beginner,  but  it 
affords  the  greatest  freedom  and  sweep,  and  many  teachers  con- 
sider it  the  only  proper  method. 

13.  Position.  The  draughtsman  should  sit  upright  and  not 
bend  over  his  drawing,  as  that  cramps  the  work  and  leads  him  to 
look,  while  working,  at  only  a small  portion  of  his  drawing  instead 
of  comprehending  the  whole  at  a glance. 

The  surface  to  receive  the  drawing  must  be  held  at  right 
angles  to  the  direction  in  which  it  is  seen,  otherwise  the  drawing 
will  be  distorted  by  the  foreshortening  of  the  surface.  A rectan- 
gular surface  such  as  a sheet  of  paper  is  at  right  angles  to  the 
direction  in  wdiich  it  is  seen  when  all  four  corners  are  equally 
distant  from  the  eye.  A fairly  accurate  test  may  be  made  in  the 
following  manner:  Locate  the  center  of  the  paper  by  drawing  the 
diagonals.  Flat  against  this  point  place  the  unsharpened  end  of  a 
pencil.  Tip  the  surface  until  the  length  of  the  pencil  disappears 
and  only  the  point  and  sharpened  end  are  visible,  then  the  surface 
will  be  at  right  angles  to  a line  drawm  from  the  eye  to  its  center. 
The  pencil  represents  this  line  for  a part  of  the  distance  because  if 
properly  held  it  is  at  right  angles  to  the  surface. 

FIRST  EXERCISES. 

Before  trying  to  draw  any  definite  forms  the  student  should 
practice  diligently  drawdng  straight  lines  in  horizontal,  vertical,  and 
• _ oblique  positions,  and  also  circles  and 

• — — *— — ' ellipses. 

14.  Straight  Lines.  In  drawing  the 
~~  | A straight  line  exercises  points  should  first  be 

placed  lightly  and  the  line  drawn  to  connect 
them  as  in  Fio*.  1.  Draw7  a series  of  ten  or  fif- 

O v 

/ / / ./  teen  lines  in  each  position,  placing  the  points 
to  be  connected  by  the  lines  one  inch  apart 
/ / and  leaving  a space  of  one  quarter  of  an 

inch  betwTeen  each  line.  Next  draw7  a series 
Points.  placing  the  points  two  inches  apart,  then  a 

group  with  the  points  four  inches  apart,  and  finally  a set  which 


! 1 


i! 


i / 


349 


10 


FREEHAND  DRAWING 


will  give  lines  eight  inches  long.  Start  to  draw  vertical  lines 
from  the  top,  horizontal  lines  from  the  left  to  right,  oblique  lines 
which  slant  upward  toward  the  right,  from  the  lower  point,  and 
those  slanting  upward  toward  the  left,  from  the  upper  point.  Use 
all  three  pencils,  3H,  F and  a solid  ink  pencil  for  these  exercises, 
and  take  the  greatest  care  not  to  press  too  strongly  on  the  paper 
with  the  harder  grades.  They  are  intended  to  make  rather  light 
gray  lines.  Where  dark  lines  are  desired  always  use  the  solid  ink 
pencil.  Try  also  making  the  exercises  with  different  widths  of 
line  regulated  by  the  bluntness  of  the  point,  and  do  at  least  one 
set  using  the  solid  ink  pencil  and  making  very  wide  lines  as  near 
together  as  is  possible  without  fusing  one  line  with  another.  In 
all  of  these  exercises  the  lines  should  each  be  drawn  with  one  pen- 
cil stroke  without  lifting  the  pencil  from  the  paper  and  absolutely 
no  corrections  of  the  line  should  be  made. 

15.  Circles  and  Ellipses.  In  practicing  drawing  circles 
start  from  a point  at  the  left  and  move  around  toward  the  right 

as  in  Fig.  2.  Draw  a series  of  ten  cir- 
cles half  an  inch  in  diameter,  forming 

o 

each  with  a single  pencil  stroke.  Next 
draw  a group  of  ten  with  a one-inch 

pencil  stroke.  Follow  these  with  a set, 
each  being  two  inches  in  diameter  and 
another  set  with  a three-incli  diameter. 
In  drawing  these  larger  circles  the  free 
arm  movement  will  be  found  necessary 
and  the  lines  may  be  swept  about  a 
number  of  times  for  the  purpose  of  correcting  the  first  outline  and 
giving  practice  in  the  arm  movement.  As  the  circles  increase  in 
diameter  the  difficulty  of  drawing  them  with  accuracy  by  a single 
stroke  increases  also,  but  instead  of  erasing  the  faulty  positions 
and  laboriously  patching  the  line,  it  is  better  to  make  the  correc- 
tions as  directed,  by  sweeping  other  lines  about  until  a mass  of 
lines  is  formed  which  gives  the  shape  correctly.  The  single  outline 
desired  will  be  found  somewhere  within  the  mass  of  lines  and  may 
be  accented  with  a darker  line  and  the  other  trial  lines  erased. 

Draw  a series  of  ten  ellipses,  Fig.  3,  with  a long  diameter  of 


diameter,  still  keeping  to  the  single 


350 


11 


FREEHAND  DRAWING 


half  an  inch,  forming  each  with  a single  pencil  stroke.  Follow 
with  a group  of  ten,  having  the  long  diameter  one  inch  in  length, 
joining  each  outline  with  a single  pencil  stroke.  Proceed  with  a 
set  having’  a long  diameter  of  two  inches  and  a set  with  a long 

o o o 

diameter  of  three  inches.  Follow  the  same  instructions  for  these 
last  two  groups  as  were  laid  down  for  drawing  the  larger  circles, 
that  is,  sweep  the  lines  about  several 
times  with  the  free  arm  movement. 

In  drawing  horizontal  straight  lines 
the  elbow  should  be  held  close  to  the 
body.  For  vertical  lines  and  for  all 
curved  lines  the  elbow  should  be  held  as 

Fig.  3.  Ellipses. 

far  from  the  body  as  possible. 

These  exercises  and  similar  ones  of  his  own  invention  should 
be  practiced  by  the  student  for  a long  period,  even  after  he  is 
studying  more  advanced  work.  Any  piece  of  waste  paper  and  any 
spare  moments  may  be  utilized  for  them.  As  in  acquiring  any 
form  of  manual  skill,  to  learn  to  draw  requires  incessant  practice, 
and  these  exercises  correspond  to  the  live-finger  exercises  which 
are  such  an  important  part  of  the  training  in  instrumental  music. 
While  they  are  not  very  interesting  in  themselves  the  training  they 
give  to  the  muscles  of  the  hand  and  arm  is  what  enables  the 
draughtsman  to  execute  his  work  with  rapidity,  ease,  and  assurance. 

The  student  should  bear  in  mind  that  a straight  freehand  line 
ought  not  to  look  like  a ruled  line.  A part  of  the  attraction  of 
freehand  drawing,  even  of  the  simplest  description,  is  the  sensi- 
tive, live  quality  of  the  line.  A straight  line  is  defined  in  geom- 
etry as  one  whose  direction  is  the  same  throughout,  but  slight 
deviations  in  a freehand  straight  line,  which  recover  themselves 
and  do  not  interfere  with  the  general  direction  are  legitimate,  as 
the  hand,  even  when  highly  trained,  is  not  a machine,  and  logically 
should  not  attempt  to  do  what  can  be  performed  with  more 
mechanical  perfection  by  instruments.  Where  freehand  straight 
lines  are  used  to  indicate  the  boundaries  of  forms,  the  slight  in- 
evitable variations  in  the  line  are  really  more  true  to  the  facts  of 
vision  than  a ruled  line  would  be,  inasmuch  as  the  edges  even  of 
geometric  solids  appear  softened  and  less  rigid  because  they  are 
affected  by  the  play  of  light  and  by  the  intervening  atmosphere. 


351 


12 


FREEHAND  DRAWING 


This  the  beginner  will  not  be  able  to  see  at  first,  for  in  this  case  as 
in  so  many  others,  his  sight  is  biased  by  his  knowledge  of  what 
the  object  is  and  how  it  feels. 

16.  Freehand  Perspective.  One  of  the  chief  difficulties  in 
learning  to  draw  is,  as  before  stated,  in  learning  to  see  correctly, 
because  the  appearance  of  objects  so  often  contradicts  what  we 
know  to  be  true  of  them.  More  than  one  beginner  has  drawn  a 
handle  on  a mug  because  he  knew  it?  was  there,  regardless  of  the 
fact  that  the  mug  was  turned  in  such  a way  that  the  handle  was 
not  visible.  The  changes  which  take  place  in  the  appearance  of 
forms  through  changes  in  the  position  from  which  they  are  seen, 
are  governed  by  the  principles  of  perspective.  Although  students 
of  this  course  are  supposed  to  be  familiar  with  the  science  of  per- 
spective, it  is  necessary  to  restate  certain  general  principles  of 
perspective  with  which  the  freehand  draughtsman  must  be  so 
familiar  that  he  can  apply  them  almost  unconsciously  as  he  draws. 
The  most  important  of  these  are  demonstrated  in  the  following 
paragraphs,  and  their  application  should  be  so  thoroughly  under- 
stood that  they  become  a part  of  the  student’s  mental  equipment. 
In  theory  the  draughtsman  draws  what  he  sees,  but  practically  he 
is  guided  by  his  knowledge  as  to  how  he  sees. 

The  principles  can  be  most  clearly  demonstrated  through  the 
study  of  certain  typical  geometric  forms  which  are  purposely 
stripped  of  all  intellectual  or  sentimental  interest,  so  that  nothing 
shall  divert  the  attention  from  the  principles  involved  in  their 
representation.  The  student  will  readily  recognize  the  great 
variety  of  subjects  to  which  the  principles  apply  and  the  impor- 
tance of  working  out  the  exercises  and  mastering  them  for  the  sake 
of  the  knowledge  they  impart.  These  principles  can  be  explained 
very  clearly  by  the  use  of  the  glass  slate,  which  is  a part  of  the 
required  outfit  for  this  course.  All  drawings  should  be  made  from 
the  models  in  outline  and  in  freehand  on  the  glass,  using  the  Cross 
pencil.  The  drawing  should  be  tested  and  corrected  according  to 
the  instructions  for  testing. 

17.  Tracing  on  the  Slate.  In  beginning  to  study  model 
drawing  the  model  may  be  traced  upon  the  slate  held  between  the 
model  and  the  eye  and  at  right  angles  to  the  direction  in  which 
the  object  is  seen.  (See  section  13.)  In  order  to  do  this  with 


352 


FREEHAND  DRAWING 


13 


accuracy  it  is  absolutely  necessary  that  the  slate  shall  not  move 
and  it  is  equally  necessary  that  the  position  of  the  eye  shall  not 
change.  As  neither  of  these  conditions  can  be  fulfilled  exactly 
without  mechanical  contrivances  for  holding  both  the  slate  and  the 
head  fixed,  it  follows  that  the  best  tracing  one' can  make  will  be 
only  approximately  correct  and  even  that  only  if  the  object  is  of  a 
very  simple  character.  The  more  complicated  the  object  the  less 
satisfactory  will  be  the  tracing  from  it.  Perhaps  the  best  method 
is  to  mark  the  important  angles  and  changes  of  direction  in  the 
contour  with  points  and  then  rapidly  connect  the  points  with  lines 
following  the  contours.  Although  the  result  may  not  be  very 
correct,  if  carefully  made  the  tracing  will  at  least  demonstrate  the 
principal  points  wherein  the  appearance  of  an  object  differs  from 
and  contradicts  the  facts,  and  that  is  the  sole  object  of  the  tracing. 
It  awakens  in  the  student  the  power  of  seeing  accurately  as  it 
teaches  the  mind  to  accept  the  image  in  the  eye  as  the  true  appear- 
ance of  an  object  even  if  that  image  differs  from  the  actual  shape 
and  proportion  of  the  object  as  we  know  it  by  the  sense  of  touch. 
Except  as  it  helps  us  to  leccrn  to  see , the  tracing  gives  no  train- 
ing in  freehand  drawing  other  than  the  slight  manual  exercise 
involved  in  drawing  the  line. 

18.  Testing  with  the  Slate.  The  great  value  of  the  slate 
for  the  beginner  in  freehand  drawing  is  the  ease  with  which  the 
accuracy  of  a drawing  may  be  tested.  To  obtain  satisfactory  re- 
sults the  models  should  be  placed  about  a foot  and  a half  in  front 
of  the  spectator  and  the  drawings  made  rather  large.  The  draw- 
ing should  be  made  freehand,  in  outline,  and  the  greatest  care 
taken  to  make  it  as  accurate  as  possible  before  testing  it  because 
the  object  in  making  the  drawing  is  to  exercise  the  hand  and  eye. 
Drawing  exercises  should  not  be  confounded  with  the  preliminary 
exercises  in  tracing  whose  only  object  is  to  emphasize  the  fact  that 
forms  appear  different  as  the  position  of  the  eye  changes. 

In  order  to  test  a drawing  place  the  slate  at  right  angles  to  a 
line  from  the  eye  to  the  model  according  to  the  directions  in  sec- 
tion 13.  Holding  the  slate  at  this  angle  and  keeping  one  eye 
closed  move  it  backward  and  forward  until  the  lines  of  the  draw- 
ing cover  the  lines  of  the  model.  Any  difference  in  the  general 
direction  of  the  lines  or  proportions  can  be  readily  observed.  Cor- 


353 


14 


FREEHAND  DRAWING 


rections  should  not  be  made  by  tracing,  but  errors  should  be  care- 
fully noted  and  the  alterations  made  freehand  from  a -re-study  of 
the  models.  If  the  drawing  is  too  large  to  cover  the  lines  of  the 
model,  errors  may  be  discovered  by  testing  the  different  angles  of 
the  drawing  with  those  of  the  model.  If  all  the  angles  coincide 
the  drawing  must  be  correct. 

In  making  the  tests  the  slate  should  be  held  firmly  with  both 
hands,  and  it  cannot  be  emphasized  too  strongly  that  the  test  is  of 
no  value  unless  the  slate  is  at  right  angles  to  the  direction  in  which 
the  model  is  seen.  When  groups  of  models  or  other  complicated 
subjects  are  being  tested  only  the  directions  of  important  lines 
and  proportions  of  leading  masses  can  be  compared.  It  must  be 
clearly  understood  that  it  takes  some  practice  and  much  care  to 
test  the  drawing  of  a simple  form,  and  that  the  slate  is'  not  to  be 
used  as  a means  of  tracing.  The  student  will  soon  discover  that 
it  is  impossible  to  trace  any  form  or  group  having  much  detail  or 
multiplication  of  parts  owing  to  the  impossibility  of  holding  the 
slate  and  the  eye  for  long  in  the  same  position  at  the  same  time. 

Do  not  expect  too  much  of  the  slate.  Even  the  first  exercises 
in  tracing  simple  forms  will  show  the  student  that  unless  he  has 
acquired  some  facility  in  making  lines  freehand  he  cannot  trace 
lines.  Indeed  it  has  often  been  observed  that  no  one  can  trace 
who  cannot  draw.  Another  difficulty  in  using  the  slate  at  first  is 
the  resistance  which  the  pencil  encounters  on  the  glass.  It  calls 
for  a different  pressure  and  touch  from  that  used  with  a pencil  on 
paper,  so  that  the  beginner  is  often  discouraged  unnecessarily  and 
becomes  impatient  with  the  slate,  partly  because  he  expects  too 
much  from  it  and  partly  because  he  has  not  learned  how  to  use  it. 
Do  not  try  to  make  perfect  lines  on  the  slate.  Be  satisfied  at  first 
to  indicate  the  general  direction  of  lines.  Understand  also  that 
the  slate  is  only  to  be  used  in  beginning  to  draw.  The  student 
should  as  soon  as  possible  emancipate  himself  from  the  use  of  the 
tests  and  depend  upon  the  eye  alone  for  judging  the  relations  of 
proportions  and  lines.  From  the  beginning  a drawing  should  be 
corrected  by  the  eye  as  far  as  possible  before  applying  any  tests. 


354 


FREEHAND  DRAWING 


15 


FREEHAND  PERSPECTIVE.* 

19.  The  Horizon  Line  or  Eye  Level.  This,  as  the  name 
implies,  is  an  imaginary  horizontal  line  on  a level  with  the  eye. 
It  is  of  great  importance  in  representation,  as  all  objects  appear 
to  change  their  shape  as  they  are  seen  above  or  below  the  horizon 
line. 


The  following1 


expe 


riments  should  be  made  before  beginning" 


to  draw  any  of  the  exercises  in  freehand  perspective.  Fasten  two 
square  tablets  together  at  right  angles  to  each  other  so  that  the 
adjacent  corners  exactly  coincide,  giving  two  sides  of  a cube. 
Hold  it  at  arm’s  length  with  the  edge  where  the  two  planes  touch, 
parallel  to  the  eyes  and  the  upper  plane  level.  Lower  it  as  far  as 
the  arms  allow,  then  raise  it  gradually  to  the  height  of  the  eyes, 
and  above  as  far  as  possible,  holding  it  as  far  out  as  possible. 
Observe  that  the  level  tablet  appears  to  become  narrower  as  it 
approaches  the  eye  level,  and  when  it  is  opposite  the  eye  it  becomes 
only  a line  showing  the  thickness  of  the  cardboard.  Observe  that 
this  line  or  front  edge  of  the  tablet  always  appears  its  actual  length 
while  the  side  edges  have  been  gradually  appearing  to  become 
shorter.  As  the  tablet  is  lifted  above  the  horizon  the  lower  side 
begins  to  appear  very  narrow  at  first,  but  widening  gradually  the 
higher  the  tablet  is  lifted.  It  will  be  seen  also  that  when  the 
tablet  is  below  the  horizon  line  the  side  edges  appear  to  run  up- 
ward, and  when  the  tablet  is  above  the  eye  its  side  edges  appear  to 
run  downward,  toward  the  horizon. 

That  they  and  similar  lines  appear  to  con  - 


JevA  o|_V  . 


r / 

\A 

1 JlliV....... 

ui 

Fig.  4.  Book 

with  Strings. 

verge  and  vanish  in  the  horizon  line  is 
proved  by  the  following  experiment: 
Place  a book  on  a table  about  two  feet 
away  with  its  bound  edge  toward  the  spec- 
tator and  exactly  horizontal  to  the  eye,  that 
is,  with  either  end  equally  distant  from  the 
eye.  Between  the  cover  and  the  first  page 
b and  as  near  the  back  as  possible  place  a 
string,  leaving  about  two  feet  of  it  on 
either  side.  Hold  the  left  end  of  the 


*Note.— 1 Thrcmgta.  the  courtesy  of  its  author  and  publishers,  these  exercises  in  free- 
hand perspective  have  been  adopted  from  the  text-book  on  “ Freehand  Drawing,”  by 
Anson  K.  Cross.  Ginn  & Co.,  Boston. 


355 


16 


FREEHAND  DRAWING 


string  in  the  right  hand  and  move  it  until  it  coincides  with  or 

Hold  the  right  end  of  the  string 


covers  the  left  edge  of  the  book. 

O 

in  the  left  hand  and  move  it  until  it  covers  the  right  edge  of  the 

O O 


two  strings  will 

O 


two  converging  or 

O O 


be  seen  to  form 
at  a point  on  the  level  of  the  eye, 


book.  The 

vanishing  lines  which  meet 
that  is,  in  the  horizon  line.  This  and  the  preceding  experiment 
illustrate  the  following  rule; 

Hide  1.  Horizontal  retreating  lines  above  the  eye  appear 
to  descend  or  vanish  downward , and  horizontal  retreating  lines 

below  the  eye  appear  to  ascend  or  vanish 
upward.  The  vanishing  point  of  any 
set  of  parallel , retreating , horizontal 
lines  is  at  the  level  of  the  eye. 

It  is  necessary  to  remember  that  the 
horizon  line  is  changed  when  the  specta- 
tor’s position  is  changed.  This  is  very 
noticeable  when  one  stands  on  a high  hill 
and  observes  that  the  roof  lines  of  houses 
which  one  is  accustomed  to  see  vanishing 
downward  to  the  level  of  the  eye,  now 
vanish  upward,  since  the  eyes  have  been 
raised  above  the  roofs. 

Retreating  lines  are  those  which  have 
one  end  nearer  the  eye  than  the  other. 

Exercise  i.  Foreshortened  Planes 
and  Lines.  Cut  from  paper  a tracing  of 
the  square  tablet,  which  is  a part  of  the 
set  of  drawing  models,  and  leave  a pro- 
jecting flap  as  at  A,  Fig.  5.  Paste  the 
flap  on  the  under  side  of  the  slate,  with 
the  edges  of  the  square  parallel  to  the 
edges  of  the  slate,  and  trace  the  actual 

o 


Holding  the  slate  vertical  and  so  that 
half  the  squave  is  above  and  half  below  the  level  of  the  eye,  turn 
the  square  somewhat  away  from  the  slate  and  trace  the  appearance. 
Turn  it  still  farther  and  trace.  Turn  it  so  that  the  surface  disap- 
pears and  becomes  a line. 


356 


FREEHAND  DRAWING 


17 


Trace  a circular  tablet  and  cut  it  out  of  paper,  leaving  a flap 
as  at  B,  Fig.  5.  Paste  tlie  flap  on  the  back  of  the  slate,  as  with  the 
square,  and  trace  its  real  appearance.  Turn  the  circle  .away  at  a 
moderate  angle  and  trace  its  appearance.  Trace  it  as  it  appears  at 
a greater  angle  and  finally  place  it  so  that  it  appears  as  a line. 

Try  similar  experiments  with  the  triangle,  the  pentagon,  and 
the  hexagon  and  observe  that  these  exercises  all  show  that  lines 
and  surfaces  under  certain  conditions  appear  less  than  their  true 
dimensions,  and  that  this  diminution  takes  place  as  soon  as  the 
surfaces  are  turned  away  from  the  glass  slate. 

When  the  square  rests  against  the  slate,  with  the  centers  of 
the  square  and  slate  coinciding,  and  the  slate  held  so  that  half  is 
above  and  half  below  the  horizon  line,  all  four  corners  of  the  square 
will  be  at  equal  distances  from  the  eye  so  that  a line  from  the  eye 
to  the  center  of  the  slate  and  of  the  square  is  at  right  angles  to  the 
surface  of  the  slate,  the  latter  represents  in  these  experiments  what 
in  scientific  perspective  is  called  the  picture  plane.  Thus  a sur- 
face or  plane  appears  its  true  relative  dimensions  only  when  it  is 
at  right  angles  to  the  direction  in  which  it  is  seen. 

It  is  for  this  reason  that  it  is  always  necessary  to  arrange  the 
surface  on  which  a drawing  is  made,  at  right  angles  to  the  eye, 
otherwise  the  surface  and  drawing  upon  it  become  foreshortened; 
that  is,  they  appear  less  than  their  true  dimensions. 

It  is  easy  to  see  from  the  drawing  of  the  foreshortened  square 
in  Fig.  4,  that  of  the  two  equal  and  parallel  lines  a b and  c d the 
nearer  appears  the  longer,  although  neither  of  the  lines  are  fore- 
shortened as  the  respective  ends  of  each  are  equally  distant  from 
the  eye.  This  illustrates  the  following  rule  : 

Rule  2.  Of  t wo  equal  and  parallel  lines , th  e nearer  appears 
tlie  longer. 

Exercise  2.  The  Horizontal  Circle.  Hold 
the  circular  tablet  horizontally  and  at  the  level  of 
the  eye.  Observe  that  it  appears  a straight  line. 

Place  the  tablet  horizontally  on  a pile  of 
books  about  half  way  between  the  level  of  the 
eye  and  the  level  of  the  table.  Trace  the  appear-  , 

ance  upon  the  slate.  circles. 

Place  the  tablet  on  the  table  and  trace  its  appearance. 


357 


is 


FREEHAND  DRAWING 


While  making  both  tracings  the  distance  between  the  eye  and 
the  object,  and  the  eye  and  the  slate  should  be  the  same. 

Hold  the  tablet  at  different  heights  above  the  level  of  the 
eye  and  observe  that  the  ellipse  widens  as  the  height  above  the  eye 
increases.  These  exercises  illustrate  the  following  rules: 

Rule  3.  A horizontal  circle  appears  a horizontal  straight 
line  when  it  is  at  a level  of  the  eye.  When  below  or  above  this 
level  the  horizontal  circle  always  appears  an  ellipse  whose  long 
axis  is  a horizontal  line. 

Rule  4.  As  the  distance  above  or  below  the  level  of  the  eye 
increases  the  ellipse  appears  to  widen.  The  short  axis  of  any 
ellipse  which  represents  a horizontal  circle  changes  its  length  as 
the  circle  is  raised  or  lowered.  The  long  axis  is  always  repre- 
sented by  practically  the  same  length  at  whatever  level  the  circle 
is  seen. 

Place  the  tablet  on  the  table  almost  directly  below  the  eye 
and  trace  its  appearance. 

Move  it  back  to  the  farther  edge  of  the  table  and  trace  it.  It 
will  be  seen  that  where  the  level  of  the  circle  remains  the  same, 
its  apparent  width  changes  with  the  distance  from  the  eye  to  the 
circle. 

Exercise  3.  Parallel  Lines.  Place  the  square  tablet  on  the 
table  1^  feet  from  the  front,  so  that  its  nearest  edge  appears  hori- 
zontal; that  is,  so  that  it  is  at  right  angles  to 
the  direction  in  which  it  is  seen.  By  tracing 
the  appearance  the  following  rules  are  illus- 

Fig.  7.  Parallel  Lines.  t rated: 

Rule  5.  Parallel  retreating  edges  appear  to  vanish , that 
is , to  converge  toward  a point. 

Rule  6.  Parallel  edges  which  are  parallel  to  the  slate,  that 
is,  at  right  angles  to  the  direction  at  which  they  are  seen,  do  not 
appear  to  co  nverge , and  any  parallel  edges  whose  ends  are  equally 
distant  from  the  eye  appear  actually  parallel. 

Exercise  4.  The  Square.  Place  the  square  tablet  as  in 
Exercise  3,  and  it  will  be  seen  that  two  of  the  edges  are  not  fore- 
shortened but  are  represented  by  parallel  horizontal  lines.  The 
others  vanish  at  a point  over  the  tablet  on  a level  with  the  eye. 

How  place  the  tablet  so  that  its  edges  are  not  parallel  to  those 


358 


FREEHAND  DRAWING 


13 


of  the  desk  and  trace  its  appearance  on  the  slate.  None  of  its 
edges  appear  horizontal,  and  when  the  lines  of  the  tracing  are  con- 
tinued as  far  as  the  slate  will  allow,  the  fact  that  they  all  converge 
will  be  readily  seen;  the  drawing  illustrates  the  following  rule  : 
Rule  7.  When  one  line  of  a right  angle  vanishes  toward 
the  right , the  other  line  vanishes  tovmrd  the  left. 

The  drawing  also  shows  that  the  edges  appear  of  unequal 
length  and  make  unequal  angles  with  a horizontal  line  and  illus- 
trates the  following  rule  : 

Rule  8.  When  two  sides  of  a square  retreat  at  unequal 
angles , the  one  which  is  more  nearly  parallel  to  the  picture  plane 
{the  slate)  appears  the  longer  and  more  nearly  horizontal. 

Exercise  5.  The  Appearance  of  Equal  Spaces  on  Any  Line. 

Cut  from  paper  a square  of  three  inches  and  draw  its  diagonals. 

Place  this  square  horizontally  in  the  middle  of 
the  back  of  the  table,  with  its  edges  parallel 
to  those  of  the  table,  and  then  trace  its  appear- 
ance and  its  diagonals  upon  the  slate.  (Fig.  8.) 
Note — The  diagonals  of  a square  bisect  each 
other  and  give  the  center  of  the  square. 

Compare  the  distance  from  the  nearer  end,  1,  of  either  diagonal  to 
the  centerof  the  square, 2,  with  thatfrom  the  centerof  the  square  to  the 
farther  end  of  the  diagonal,  3,  for  an  illustration  of  the  following  rule: 
Rule  9.  Equal  distances  on  any  retreating  line  appear 
unequal,  the  nearer  of  any  two  appearing  the  longer. 

Exercise  6.  The  Triangle.  Draw  upon  an  equilateral  tri- 
angular tablet  a line  from  an  angle  to  the  center  of  the  opposite 
side.  (This  line  is  called  an  altitude.) 

Connect  the  triangular  tablet  with  the 

o 

square  tablet,  and.  place  them  on  the  table  so 
that  the  base  of  the  triangle  is  foreshortened, 
and  its  altitude  is  vertical.  Trace  the  triangle 
and  its  altitude  upon  the  slate.  The  tracing 
illustrates  the  fact  that  the  nearer  half  of  a re- 
ceding line  appears  longer  than  the  farther  Fig  9 The  Triangle, 
half  (see  Pule  9),  and  also  the  following  rule: 

Ride  10.  The  upper  angle  of  a vertical  isosceles 
or  equilateral  triangle , whose  base  is  horizontal,  appears 


Fig.  8.  Equal  Space 
on  any  Line. 


359 


20 


FREEHAND  DRAWING 


in  a vertical  line  erected  at  the-  perspective  center  of  the  base. 

Exercise  7.  The  Prism.  Connect  two  square  tablets  by  a 
rod  to  represent  a cube,  and  bold  the  object  so  that  one  tablet  only 
is  visible,  and  discover  that  it  must  appear  its  real  shape,  A,  Fig.  10. 
This  illustrates  the  following;  rule: 

Rule  11.  When  one  face  only  of  a prism  is  visible,  it 
appears  its  * eal  shape. 

Place  the  cube  represented  by  tablets  (Fig.  10)  in  the  middle 
of  the  back  of  the  desk,  and  trace  its  appearance.  First,  when  two 


Fig.  10.  The  Prism. 


faces  only  of  the  solid  would  be  visible  (B);  and,  second,  when 
three  faces  would  be  seen  (C).  These  tracings  illustrate  the  fol- 
lowing rule: 

Rule  12.  When  two  or  more  faces  of  a cube  are  seen , none 
of  them  can  appear  their  real  shapes. 

Place  the  cubical  form  on  the  desk,  with  the  tablets  vertical, 
and  one  of  them  seen  edgewise  (D)  and  discover  that  the  other 
tablet  does  not  appear  a straight  line.  This  illustrates  the  follow- 
ing rule: 

o 

Rule  13.  Only  one  end  of  a prism  can  appear  a straight 
line  at  any  one  time. 

Exercise  8.  The  Cylinder.  Connect  two  circular  tablets  by 
a 2A-inch  stick,  to  represent  the  cylinder.  Hold  the  object  so  that 
one  end  only  is  visible,  and  see  that  it  appears  a circle  (Fig.  11). 

Place  the  object  on  the  table,  so  that  its  axis  is  horizontal 
but  appears  a vertical  line,  and  trace  its  appearance.  The  tracing 
illustrates  the  following  rule: 

Rule  14.  When  an  end  and  the  curved  surface  of  a cylin- 
der are  seen  at  the  same  time , the  end  must  appear  an  ellipse 
(Fig.  12). 


360 


FREEHAND  DRAWING 


21 


Place  the  object  horizontally,  and  so  that  one  end  appears  a 
vertical  line,  and  trace  to  illustrate  the  following  rule: 


Rule  15.  When  one  end  of  a cylinder  appears  a straight 
line , the  other  appears  an  ellipse.  ( Fig . 13.) 

Place  the  object  upright  on  the  table,  and  trace  its  ends  and 
axis.  Draw  the  long  diameters  of  the  ellipse,  and  discover  that 
they  are  at  right  angles  to  the  axis  of  the  cylinder.  This  illustrates 
the  following  rule: 

Ride  16.  The  bases  of  a vertical  cylinder  appear  horizontal 
ellipses.  The  nearer  base  always  appears  the  narrower  ellipse. 
{Fig.  14.) 

Place  the  object  with  its  axis  horizontal  and  at  an  angle,  so 
that  the  surfaces  of  both  tablets  are  visible.  Trace  the  tablets 

and  the  rod,  and  then  draw  the 
long  diameters  of  the  ellipses,  and 
discover  that  they  are  at  right 
angles  to  the  axis  of  the  cylindrical 
form.  The  axes  of  the  ellipses  are 
inclined,  and  the  drawing;  illus- 

o 

trates  the  following  rules: 

Rule  17.  The  bases  of  a 

tode'r-uprigh?'  F1£ilisTHOTifin“aa!r  oyVmder  appear  ellipses,  whose 
and  at  an  Angie.  iong  diameters  are  at  right  angles 

to  the  axis  of  the  cylinder , the  nearer  base  appearing  the  nar- 
rower ellipse. 

Note.— The  farther  end  may  appear  narrower  than  the  nearer, 
but  must  always  appear  proportionally  a wider  ellipse  than  the 
nearer  end. 


361 


22 


FREEHAND  DRAWING 


Rule  18.  Vertical  foreshortened  circles  below  or  above  the 
level  of  the  eye  appear  ellipses  whose  axes  are  not  vertical  lines. 

Ride  19.  The  long  axis  of  an  ellipse  representing  a ver- 
tical circle  below  or  above  the  level  of  the  eye  is  at  right  angles 
to  the  axis  of  a cylinder  of  which  the  circle  is  an  end. 

Rule  20.  The  .< elements  of  the  cylinder  appear  to  converge 
in  the  direction  of  the  invisible  end.  This  convergence  is  not 
represented  when  the  cylinder  is  vertical. 

Note  i. — Less  than  half  the  curved  surface  of  the  cylinder  is 
visible  at  any  one  time. 

Note  2 — The  elements  of  the  cylinder  appear  tangent  to  the 
bases  and  must  always  be  represented  by  straight  lines  tangent  to 
the  ellipses  which  represent  • the  bases.  When  the  elements  con- 
verge, the  tangent  points  are  not  in  the  long  axes  of  the  ellipses. 

See  Fig.  12,  in  which  if  a straight  line  tangent 
to  the  ellipse  be  drawn,  the  tangent  points  will 
be  found  above  the  long  axes  of  the  ellipses. 

Exercise  9.  The  Cone.  Hold  the  cone  so 
that  its  axis  is  directed  toward  the  eye,  and  the  cone  appears  a 
circle.  Hold  the  cone  so  that  its  base  appears  a straight  line,  and 
it  appears  a triangle.  (Fig-  16.) 

Place  a circular  tablet,  Fig.  17,  having  a rod 
attached,  to  represent  the  axis  of  the  cone,  so  that  the 
axis  is  first  vertical  and  second  inclined.  Trace  both 
positions  of  the  object,  and  discover  that  the  appear- 
ance of  the  circle  is  the  same  as  in  the  case  of  the 
cylinder.  The  tracings  illustrate  the  following  rule: 
Rule  21.  When  the  base  of  the  cone  appears 
an  ellipse , the  long  axis  of  the  ellipse  is  p>erpen- 
dicular  to  the  axis  of  the  cone. 

Note  1 — More  than  half  the  curved  surface  of 
the  cone  will  be  seen  when  the  vertex  is  nearer  the  eye  than  the 
base,  and  less  than  half  will  be  seen  when  the  base  is  nearer  the  eye 
than  the  vertex.  The  visible  curved  surface  of  the  cone  may  range 
from  all  to  none. 

Note  2 The  contour  elements  of  the  cone  are  represented  by 

straight  lines  tangent  to  the  ellipse  which  represents  the  base,  and 

on  1 r 

the  points  of  tangency  are  not  in  the  long  axis  of  this  ellipse. 


Fig.  17.  The 
Cone—Tablet 
with  Rod. 


Fig.  16.  The  Cone. 


30« 


FREEHAND  DRAWING 


23 


Exercise  10.  The  Regular  Hexagon.  In  Fig.  18  the  opposite 
sides  are  parallel  and  equal.  The  long  diagonal  A D is  parallel  to 
the  sides  B C and  E F,  and  it  is  divided  into  four  eijual  parts  by 
the  short  diagonals  B F and  C E,  and  by  the  long  diagonals  B E 
or  C F. 


The  perspective  drawing  of  this  figure  will  be  corrected  by 
giving  the  proper  vanishing  to  the  different  sets  of  parallel  lines, 
and  by  making  the  divisions  on  the  diagonal  A 1)  perspectively 
equal. 

Draw  the  long  and  short  diagonals  upon  a large  hexagonal 

o o I o o 

tablet.  Place  this  tablet  in  a horizontal  or  vertical  position,  Fig. 
19,  and  then  trace  upon  the  slate  its  appearance  and  the  lines  upon 
it.  The  tracing  illustrates  the  following  rule: 

Rule  22.  In  a correct  drawing  of  the  regular  hexagon , any 
long  diagonal  when  intersected  by  a long  diagonal  and  two  short 
diagonals,  will  be  divided  into  four  equal  parts. 

Exercise  ii.  The  Center  of  the  Ellipse  Does  Not  Represent 
the  Center  of  the  Circle.  Cut  from  paper  a square  of  three  inches, 
after  having  inscribed  a circle  in  the  square.  Draw  the  diameters 
of  the  square  and  then  place  the  square  horizontally  at  the  middle 


Fig.  20.  Center  of  Circle  not  Fig.  21.  Concentric  Circles. 

Center  of  Ellipse. 

of  the  back  of  the  table,  with  its  edges  parallel  to  those  of  the  table. 
Trace  the  square,  its  diameters,  and  the  inscribed  circle,  upon  the 
slate.  The  circle  appears  an  ellipse,  and  as  the  long  axis  of  an 
ellipse  bisects  the  short,  it  is  evident  that  it  must  come  below  the 


363 


24 


FREEHAND  DRAWING 


center  of  the  square,  and  we  discover  that  the  center  of  the  ellipse 
does  not  represent  the  center  of  the  circle,  and  that  the  diameter  of 
the  circle  appears  shorter  than  a chord  of  the  circle. 

Exercise  12.  Concentric  Circles.  Cut  a 4-inch  square  from 
practice  paper,  and  draw  the  diagonals.  With  the  center  of  the 
square  as  center  draw  two  concentric  circles,  4 inches  and  2 inches 
in  diameter. 

Place  the  card  horizontally  upon  the  table,  as  illustrated,  and 
trace  its  appearance  upon  the  slate,  together  with  all  the  lines 
drawn  upon  it. 

Draw  the  vertical  line  which  is  the  short  axis  of  both  ellipses. 
Bisect  the  short  axis  of  the  outer  ellipse,  and  draw  the  long  axis 
of  this  ellipse.  Bisect  the  short  axis  of  the  inner  ellipse,  and  draw 
its  long  axis.  It  will  be  seen  that  the  long  axes  are  parallel  but 
do  not  coincide,  and  that  both  are  in  front  of  the  point  which  rep- 
resents the  center  of  the  circles. 

Each  diameter  of  the  larger  circle  is  divided  into  four  equal 
parts.  The  four  equal  spaces  on  the  diameter  which  forms  the 
short  axis  appear  unequal,  according  to  Rule  9.  The  diameter 
which  is  parallel  to  the  long  axes  of  the  ellipses  has  four  equal 
spaces  upon  it,  and  they  appear  equal.  This  diameter  is  behind 
the  long  axes,  but  generally  a very  short  distance;  and  in  practice, 
if  the  distance  1 2 between  the  ellipses  measured  on  the  long  axis 
is  one-fourth  of  the  entire  long  axis,  then  the  distance  between  the 
ellipses  measured  on  the  short  axis  must  be  a perspective  fourth 
of  the  entire  short  axis.  This  illustrates  the  following  rule: 

Rule  23.  Foreshortened  concentric  circles  appear  ellipses 
whose  short  axes  coincide.  The  distance  between  the  ellipses  on 
the  short  axis  is  perspectively  the  same  proportion  of  the  entire 
short  axis , as  the  distance  between  the  ellipses  measured  on  the 
long  axis , is  aeometrically  the  same  p>roportion  of  the  entire 
long  axis. 

Exercise  13.  Frames.  In  the  frames  are  found  regular  con- 
centric polygons  with  parallel  sides,  the  angles  of  the  inner  poly- 
gons being  in  straight  lines  connecting  the  angles  of  the  outer 
polygon  with  its  center.  In  polygons  having  an  even  number  of 
sides,  the  lines  containing  the  angles  of  the  polygons  form  diagon- 
als of  the  figure,  as  in  the  square. 


364 


FREEHAND  DRAWING 


25 


In  polygons  having  an  odd  number  of  sides,  the  lines  con- 
taining the  angles  of  the  polygon  are  perpendicular  to  the  sides 
opposite  the  angles,  as  in  the  triangle. 

Di  ’aw  upon  large  triangular  and  square  tablets  the  lines 
shown  in  Fig.  22.  Place  the  tablets  horizontally  on  the  table,  or 
support  them  vertically,  and  trace  upon  the  slate  the  appearance 


of  the  edges  and  all  the  lines  drawn  upon  them.  The  tracings 
illustrate  the  following;  rule: 

Rule  24.  In  representing  the  regular  frames , the  angles 
of  the  inner  figure  must  he  in  straight  lines  passing  from  the 
angles  of  the  outer  figure  to  the  center.  These  lines  are  alti- 
tudes or  diagonals  of  the  polygons. 

20.  After  making  the  tracings  described  in  the  foregoing 
exercises,  draw  (not  trace)  freehand  on  the  slate  the  various  tab- 
lets, arranged  to  illustrate  each  one  of  the  exercises.  This  is  really 
drawing  from  objects,  and  where  the  rods  are  used  to  connect  the 
tablets  the  figures  are  equivalent  to  geometric  solids.  After  the 
proportions  of  the  surfaces  are  correctly  indicated,  lines  connect- 
ing the  corresponding  corners  of  the  tablets  should  be  drawn  to 
complete  the  representation  of  solid  figures.  The  lines  indicating 
the  rods  and  those  lines  which  in  a solid  form  would  naturally  be 
invisible,  maybe  erased.  By  the  use  of  the  three  rods  of  different 
lengths,  three  figures  of  similar  character  but  different  proportions 
may  be  obtained.  These  should  each  be  drawn,  but  each  in  a dif- 
ferent position. 

The  following  directions,  which  are  based  on  general  prin- 
ciples, apply  to  all  drawing  whether  from  objects  or  from  the  flat, 
for  work  in  pencil  or  in  any  other  medium;  drawing  from  another 
drawing,  a photograph  or  a print,  whether  at  the  same  size  or 
larger,  is  called  working  from  the  fiat. 


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21.  General  Directions  for  Drawing  Objects.  First  observe 
carefully  the  whole  mass  of  the  object,  its  general  proportions  and 
the  direction  of  lines  as  well  as  the  width  of  the  angles.  Then 
sketch  the  outlines  rapidly  with  very  light  lines,  and  take  care  that 
all  corrections  are  made,  not  by  erasing  but  by  lightly  drawing 
new  lines  as  in  Fig.  23.  By  working  in  this  manner  much  time 
is  saved  and  the  drawing  gains  in  freedom.  Where  the  drawing 
is  kept  down  to  only  one  line  which  is  corrected  by  erasure,  the 

line  becomes  hard  and  wiry,  and 
there  is  a tendency  to  be  satisfied 
with  something  inaccurate  rather 
than  erase  a line  which  has  taken 
much  time  to  produce.  There  is 
always  a difficulty  at  first  in  draw- 
ing lines  light  enough,  and  it  is 
well  for  the  beginner  to  make  the 
first  trial  lines  with  a rather  hard 
pencil.  Practice  until  the  habit  of 
sketching  lines  lightly  is  fixed. 
The  ideal  is  to  be  able  to  set  down 
exact  proportions  at  the  first  touch. 
This,  however,  is  attained  by  com- 
paratively few  artists,  and  only 
after  long  study,  but  the  student 
will  soon  find  himself  able  to  ob- 
tain correct  proportions  with  only  a few  corrections. 

22.  It  cannot  be  too  strongly  emphasized  that  the  student 
must  teach  himself  to  regard  the  subject  he  is  depicting,  as  a whole, 
and  to  put  down  at  once  lines  that  suggest  'the  outline  of  the 
whole.  This  he  will  find  contrary  to  his  inclination,  which  with 
the  beginner  is  always  to  work  out  carefully  one  part  of  the  draw- 
ing before  suggesting  the  whole. 

There  are  two  objections  to  this  ; in  the  first  place,  much  time 
having  been  spent  on  one  part,  it  is  almost  inevitable  that  the  addi- 
tion of  other  portions  reveals  faults  in  the  completed  part,  and  un- 
necessary time  is  consumed  in  correcting.  The  second  objection  is 
that  a drawing  made  piecemeal  is  sure  to  have  a disjointed  look, 
even  if  the  details  are  fairly  accurate  in  their  relative  proportions. 


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27 


The  idea  of  unity  is  lost  and  some  one  detail  is  apt  to  assume  un- 
due importance,  instead  of  all  details  being  subordinated  to  the 
general  effect  of  the  whole.  It  is  always  most  important  to  state 
the  general  truths  about  the  subject  rather  than  small  particular 
truths,  which  impair  the  general  statement.  This  applies  particu- 
larly to  small  variations  in  the  outline  which  should  be  omitted 
until  the  big  general  direction  or  shape  has  been  established. 

23.  Where  an  outline  drawing  is  desired,  after  the  correct 
lines  have  been  found,  they  should  be  made  stronger  than  the 
others  and  then  all  trial  lines  erased.  In  doing  this  the  eraser  will 

o 

usually  remove  much  of  the  sharpness  of  the  correct  lines  so  that 
only  a faint  indication  of  the  desired  result  remains.  These  should 
be  strengthened  again  with  a softer  pbncil  and  each  line  produced, 
as  far  as  possible,  directly  with  one  touch  ; in  the  case  of  curves 
and  very  long  lines,  breaking  the  line  and  beginning  a new  one  as 
near  as  possible  to  the  end  of  the  previous  line,  but  taking  care 
that  the  lines  do  not  lap. 

As  soon  as  the  student  has  acquired  some  proficiency  in  draw- 
ing the  single  figures  made  from  the  tablets,  groups  of  two  or 
three  objects  should  be  attempted.  Combinations  of  books  or  boxes 
with  simple  shapes,  or  vases,  tumblers,  bowls  and  bottles  will  illus- 
trate most  of  the  principles  involved  in  freehand  perspective. 
Outline  sketches  may  be  made  on  the  slate  first  and  tested  in  the 
usual  way,  and  afterward  the  same  group  may  be  drawn  larger  on 
paper.  The  chief  difficulty  in  drawing  a group  is  to  obtain  the  rela- 
tive proportions  of  the  different  objects.  There  is  the  same  objec- 
tion to  completing  one  object  and*  then  another  as  there  is  to 
drawing  a single  object  in  parts.  The  whole  group  must  be  sug- 
gested at  once.  This  can  best  be  done  by  what  is  called  blocking 
in,  by  lines  which  pass  only  through  the  principal  points  of  the 
group.  The  block  drawing  gives  hardly  more  than  the  relative 
height  and  width  of  the  entire  group  and  the  general  direction  of 
its  most  important  lines.  But  if  these  are  correct,  the  subdivision 
of  the  area  within  into  correct  proportions  is  not  difficult.  The 
longer  and  more  important  lines  of  the  parts  are  indicated  and 
short  lines  and  details  lost. 

24.  Testing  Drawings  by  Measurement.  In  drawings  which 
are  not  made  on  the  slate  the  following  method  of  testing  propor- 


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. tions  is  usual.  WMh  the  arm  stretched  forward  to  its  greatest 
length,  hold  the  pencil  upright  so  that  its  unsharpened  end  is  at 
the  top.  Move  it  until  this  end  coincides  with  the  uppermost  point 
of  the  object.  Holding  it  fixed  and  resting  the  thumb  against  the 
pencil,  move  the  thumb  up  and  down  until  the  thumb  nail  marks 
the  lowest  point  of  the  object.  The  distance  measured  off  on  the 
pencil  represents  the  upright  dimension.  Holding  the  pencil  at 
exactly  the  same  distance  from  the  eye,  turn  it  until  it  is  horizon- 
tal and  the  end  of  the  pencil  covers  the  extreme  left  point  of  the 
object.  Should  the  height  and  width  be  equal,  the  thumb  nail 
would  cover  the  extreme  right  edge  of  the  object.  If  the  width  is 
greater  than  the  height,  use  the  height  as  a unit  of  measurement 
and  discover  the  number  of  times  it  is  contained  in  the  width. 
Always  use  the  shorter  dimension  as  the  unit  of  measurement. 
The  accuracy  of  the  test  demands  that  the  pencil  should  be  at  ex- 
actly the  same  distance  from  the  eye  while  comparing  the  width 
and  height.  In  order  to  insure  this,  the  arm  must  not  be  bent  at 
the  elbow  and  must  be  stretched  as  far  as  possible  without  turning 
the  body,  which  must  not  move  during  the  operation.  The  dis- 
tance from  the  eye  to  the  object  must  not  change  during  the  test, 
and  the  position  of  the  eye  and  body  is  first  fixed  by  leaning  the 
shoulders  firmly  against  the  back  of  the  chair  and  keeping  them  in 
that  position  while  the  test  is  taking  place.  It  is  equally  impor- 
tant in  both  the  upright  and  horizontal  measurement  that  the  pen- 
cil be  held  exactly  at  right  angles  to  the  direction  in  which  the 
object  is  seen ; i.e.,  at  right  angles  to  an  imaginary  line  from  the 
eye  to  the  center  of  the  object.  In  either  position  the  two  ends  of 
the  pencil  will  be  equally  distant  from  the  eye.  The  test  should 
be  made  several  times  in  order  to  insure  accuracy,  as  there  is  sure 
to  be  some  slight  variation  in  the  distances  each  time.  Avoid  tak- 
ing  measurements  of  minor  dimensions,  as  the  shorter  the  distances 
measured  the  more  inaccurate  the  test  becomes.  At  the  best  meas- 
urements obtained  in  this  way  are  only  approximately  correct,  and 
too  much  care  cannot  be  taken  in  order  to  render  the  test  of  use. 
Applied  carelessly,  the  test  is  not  only  valueless,  but  thoroughly 
misleading.  Wrhen  there  is  any  great  conflict  between  the  appear- 
ance of  the  object  and  the  drawing  after  it  has  been  corrected  by 
the  test,  it  is  often  safe  to  assume  some  mistake  in  applying  the 


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29 


test  and  to  trust  the  eye.  In  such  a case  the  test  may  be  tested  by 
the  use  of  the  slate.  A few  lines  and  points  will  be  sufficient  to 
indicate  the  width  and  height  on  the  slate,  and  the  relative  propor- 
tions can  then  be  calculated. 

The  plumb-line  affords  another  method  of  testing.  A thread 
or  a string  with  any  small  object  for  a weight  attached  to  one  end, 
is  sufficient.  Hold  the  string  so  that  it  hangs  vertical  and  motion- 
less, and  at  the  same  time  covers  some  important  point  in  the  ob- 
ject. By  looking  up  and  down  the  line  the  points  directly  over  and 
under  the  given  point  can  be  determined  and  the  relative  distances 
of  other  important  points  to  the  right  and  left  can  be  calculated. 
The  plumb-line  will  also  determine  all  the  vertical  lines  in  the 
object  and  help  to  determine  divergence  of  lines  from  the  vertical. 

A ruler,  a long  rod,  or  pencil  held  in  a perfectly  horizontal 
position  is  also  of  assistance  in  determining  the  width  of  angles 
and  divergences  of  lines  from  the  horizontal. 

25.  Misuse  of  Tests.  The  use  of  tests  may  easily  be  per- 
verted and  become  mischievous.  Since  the  object  of  all  draw- 
ing is  to  train  the  hand  and  eye,  it  follows  naturally  that  the  more 
the  student  relies  upon  tests  the  less  will  he  depend  upon  his  per- 
ceptions to  set  him  right,  and  the  less  education  will  he  be  giving 
to  his  perceptions.  There  is  no  greater  mistake  for  a student  than 
to  use  the  measuring  test  before  making  a drawing.  Spend  any 
amount  of  time  in  calculating  relative  proportions  by  the  eye,  but 
put  these  down  and  correct  them  by  the  eye,  not  once  but  many 
times  before  resorting;  to  tests.  All  the  real  education  in  drawing 
takes  place  before  the  tests  are  made.  Let  the  student  remember 
that  the  tests  may  help  him  to  make  an  accurate  drawing,  but  they 
will  never  make  him  an  accurate  draftsman  in  the  true  sense. 
Nothing  but  training  the  eye  to  see  and  the  hand  to  execute 
what  the  eye  sees,  will  do  that.  When  the  student  has  reached 
the  end  of  his  knowledge,  has  corrected  by  the  eye  as  far  as  he 
can,  then  by  applying  tests  he  is  enabled  to  see  how  far  his  percep- 
tions have  been  incorrect.  That  is  the  only  educational  value  of 
the  test.  Merely  to  make  an  accurate  drawing  with  as  little  men- 
tal effort  as  possible,  relying  upon  test  measurements,  requires 
considerable  practice  and  skill  in  making  the  tests,  but  gives  very 
little  practice  or  training  in  drawing. 


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26.  Light  and  Shade.  Objects  in  nature,  as  before  explained, 
detach  themselves  from  each  other  by  their  differences  in  color  and 
in  light  and  shade. 

In  drawing  without  color,  artists  have  always  allowed 
themselves  a very  wide  range  in  the  amount  of  light  and  shade 
employed,  extending  from  drawing  in  pure  outline  up  to  the 
representation  of  exact  light  and  shade,  or  of  true  values,  as  it  is 
called. 

Drawings  which  contain  light  and  shade  may  be  divided  into 
two  classes:  Form  drawing,  which  is  from  the  point  of  view  of 

the  draftsman,  and  value  drawing,  which  is  from  the  point  of  view 
of  the  painter. 

27.  Form  Drawing.  In  form  drawing  the  chief  aim,  as  the 
name  implies,  is  to  express  form  and  not  color  and  texture.  In 
order  to  do  this,  shadows  and  cast  shadows  are  indicated  only  as 
far  ^s  they  help  to  express  the  sl^ape.  This  is  the  kind  of  drawing 
practiced  by  most  of  the  early  Italian  masters,  and  it  has  been 
called  the  Florentine  method.  It  is  often  a matter  of  careful  out- 
line with  just  enough  shadow  included  to  give  a correct  general 
impression  of  the  object.  There  is  usually  little  variety  in  the 
shadow  and  no  subtle  graduations  of  tone,  but  the  shadows  are 
indicated  with  sufficient  exactness  of  shape  to  describe  the  form 
clearly.  Form  drawing  is  a method  of  recording  the  principal 
facts  of  form  with  rapidity  and  ease  and  of  necessity  deals  only 
with  large  general  truths.  Perhaps  its  most  distinguishing  feature 
is  that  it  does  not  attempt  to  suggest  the  color  of  the  form. 

28.  Value  Drawing.  The  word  value  as  it  is  used  in  draw- 
ing is  a translation  from  the  French  word  valeur , and  as  used  by 
artists  it  refers  to  the  relations  of  light  and  dark. 

Value  drawing  represents  objects  exactly  as  we  see  them  in 
nature;  that  is,  not  as  outline,  but  as  masses  of  lights  and  darks. 
In  value  drawing  the  artist  reproduces  with  absolute  truth  the  dif- 
ferent degrees  of  light  and  shade.  While  form  drawing  suggests 
relief,  value  drawing  represents  it,  and  it  also  represents  by  trans- 
lating them  into  their  corresponding  tones  of  gray,  the  values  of 
color.  In  form  drawing,  a draftsman  representing  a red  object 
and  a yellow  one,  would  be  satisfied  to  give  correct  proportions 
and  outlines  with  one  or  two  principal  shadows,  while  a value 


370 


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31 


drawing  of  the  same  objects  would  show  not  only  the  relation  of 
the  shadows  as  they  are  in  nature,  but  also  the  further  truth  that 
the  red  object  was  as  a whole  darker  than  the  yellow  one.  The 
light  side  of  the  red  object  might  even  be  found  to  be  darker  in 
value  or  tone  than  the  shadow  side  of  the  yellow  form. 

29.  Values.  Drawing  has  been  called  the  science  of  art, 
but  artists  have  rarely  approved  the  introduction  of  scientific 
methods  in  the  study  of  drawing,  fearing  lest  the  use  of  formulas 
should  lead  to  dull  mechanical  results.  Students  are  left  to  discover 
methods  and  formulas  of  their  own.  It  is  true  that  every  success- 
ful draftsman  or  artist  has  a method  which  he  has  worked  out  for 
himself,  but  he  usually  feels  it  to  be  so  much  a matter  of  his  own 
individuality,  that  he  is  reluctant  to  impose  it  on  students,  who  are 
likely  to  confound  what  is  a vital  principle  with  a personal  man- 
nerism, and  by  imitation  of  the  latter  injure  the  quality  of  personal 
expression  which  is  so  important  in.  all  creative  work.  So  there  is 
an  inclination  among  drawing  teachers  to  distrust  anything  which 
tends  even  to  formulate  the  principles  of  drawing.  Recently  there 
has  been,  however,  a distinct  advance  in  the  study  of  these  prin- 
ciples, under  the  leadership  of  Dr.  Denman  AV.  Ross,  of  Harvard 
University,  who  has  made  it  possible  for  the  first  time  to  speak 
with  exactness  of  colors  and  values.  As  Dr.  Ross  has  permitted 
the  use  of  his  valuable  scale  in  this  text  book,  it  will  greatly  assist 
in  making  tangible  and  clear,  what  would  otherwise  be  obscure 
and  difficult  to  explain. 

The  word  values  as  used  in  the  text  book  refers  entirely  to 
relations  of  light  and  dark.  For  instance,  the  value  of  a given  col- 
or,  is  represented  by  a tone  of  gray  which  has  the  same  density  or 
degree  of  light  and  dark  that  the  color  has.  The  value  of  a spot  of 
red  paint  on  a white  ground  is  expressed  by  a spot  of  gray  paint 
which  appears  as  dark  on  the  white  ground  as  does  the  red  paint, 
but  from  which  the  color  principle  has  been  omitted.  A good  pho- 
tograph of  a colored  picture  gives  the  values  of  the  picture.  A poor 
photograph,  on  the  contrary,  distorts  the  values  and  blues  are  often 
found  too  light,  while  reds  and'  yellows  will  be  too  dark  to  truth- 
fully express  the  values  of  the  original  color. 

30.  The  Value  Scale.  All  possible  values  which  can  be  rep- 
resented in  drawing,  lie  between  the  pure  whites  of  paper  or  pig- 


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FREEHAND  DRAWING 


merits  and  the  pure  black  of  pen- 
cil, ink,  or  other  pigments.  In 
order  to  think  or  speak  precisely 
of  the  great  range  of  values  be- 
tween  black  and  white,  it  is 
necessary  that  they  shall  be  clas- 
sified in  some  way.  It  is  not 
sufficient  to  say  that  a given 
shadow  is  light,  or  medium,  or 
dark  in  value.  Dr.  Ross  has 
overcome  the  difficulty  by  ar- 
ranging a value  scale  of  nine 
equal  intervals,  which  covers  the 
whole  range  from  pure  white  to 
pure  black.  Each  interval  has 
its  appropriate  designation  and 
a convenient  abbreviation.  This 
scale  affords  a practical  working 
basis  for  the  study  of  values.  It 
is  evident  that  while  the  indi- 
vidual scale  does  not  include  all 
possible  values,  it  can  readily  be 
enlarged  indefinitely  by  intro- 
ducing values  between  those  of 

O 

the  scale  as  described.  As  a 
matter  of  fact,  any  differences  in 
value  that  might  come  between 
any  two  intervals  of  the  scale 
would  rarely  be  represented,  as 
it  is  the  practice  in  drawing  to 
simplify  values  as  much  as  pos- 
sible; that  is  to  consider  the 
general  value  of  a mass,  rather 
than  to  cut  it  up  into  a number 
of  slightly  varying  tones  which 
are  not  necessary  for  expressing 
anything  of  importance  in  the 
object. 


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FREEHAND  DRAWING 


33 


31.  How  to  Make  a Value  Scale.  Fig.  24  shows  a value 
scale  with  the  names  of  the  intervals  and  their  abbreviations.  In 
making  a value  scale  the  student  should  work  in  pencil,  confining 
each  interval  within  a circle  three-quarters  of  an  inch  in  diameter. 
White  will  be  represented  by  the  white  paper  with  a circle  penciled 
about  it.  Black  (B)  and  white  (W)  should  be  established  first, 
then  the  middle  value  (M),  light  (L)  and  dark  (D) ; afterward  the 
remaining  values,  low  light  (LL),  high  light  (HL),  low  dark  (LD) 
and  high  dark  (HD). 

32.  How  to  Use  a Value  Scale.  When  the  objects  to  be 
drawn  are  neutral  in  color,  that  is,  are  black,  white,  or  gray,  the 
relative  values  are  perceived  without  special  difficulty.  When  the 
objects  are  in  color,  the  draftsman  is  obliged  to  translate  the  color 
element  into  terms  of  light  and  dark. 

I*n  order  to  determine  the  value  of  any  surface,  it  is  a help  to 
compare  the  surface  with  a piece  of  white  paper  held  in  such  a way 
that  it  receives  the  greatest  amount  of  light.  It  not  infrequently 
happens  that  two  surfaces  quite  different  in  color  will  be  of  exactly 
the  same  value.  The  student  should  make  a practice  of  observing 
the  relative  values  of  things  about  him,  even  when  he  is  not  engaged 
in  drawing. 

Place  a sheet  of  white  paper  in  the  sunlight  as  it  falls  through 
a window  and  compare  its  value  with  that  of  white  paper  further 
in  the  room  and  outside  of  the  sunlight.  Try  a similar  experiment 
with  black.  These  merely  show  what  everyone  may  suppose  that 
he  knows  already — that  the  less  light  a surface  receives  the  darker 
value  it  appears  to  have.  As  a matter  of  fact,  beginners  are  more 
ready  to  accept  this  truth  with  regard  to  color  than  they  are  when 
it  relates  to  black  and  white. 

An  instructive  way  of  studying  values  is  to  look  through  a 
closed  window  and  compare  the  values  of  forms  outside  to  the  value 
of  the  window  sash.  Even  when  the  sash  is  painted  white,  it  will 
often  be  observed  to  appear  darker  than  any  shadow  out  of  doors. 

33.  General  Directions  for  Drawing  the  Examination 
Plates.  The  examination  plates  are  planned  to  give  as  great  a 
variety  to  the  style  of  drawing  as  possible.  The  architect  is  called 
upon  to  use  freehand  drawing  in  two  general  ways;  to  make  work- 
ing drawings  of  ornament,  either  painted  or  carved,  and  to  make, 


373 


FREEHAND  DRAWING 


34 


for  reference,  sketches  or  notes,  more  or  less  elaborate,  from  orna- 
ment already  in  existence,  or  from  buildings  either  entire  or  in 
part,  as  well  as  from  their  landscape  setting.  This  course  will  not 
include  drawing  of  architecture  and  landscape. 

In  making  a working  drawing  of  ornament  every  shape  and 
curve  should  be  drawn  to  perfection,  with  clean,  careful  lines,  in 
order  that  there  shall  be  no  opportunity  for  the  craftsman  who 
executes  the  work  to  interpret  it  differently  from  the  designer’s 
intention.  Light  and  shade  are  used  sparingly  as  the  exact 
amount  of  relief  is  indicated  by  sections. 

In  making  sketches  or  notes,  while  proportions  must  be  accu- 
rately studied,  form  may  be  suggested  by  a much  freer  quality  of 
line.  In  a working  drawing  light  and  shade  maybe  merely  indi- 
cated or  may  be  carried  to  any  degree  of  elaboration.  The  natural 
way  of  teaching  this  kind  of  drawing  is  to  work  from  the  objects 
themselves  or  from  casts.  This  is  not  possible  in  a correspondence 
course,  but  all  the  principles  of  sketching  may  be  very  well  taught 
by  drawing  from  photographs  of  ornament,  and  this  method  has 
some  decided  advantages  of  its  own  for  a beginner.  The  light 
and  shade  in  the  photograph  are  fixed,  while  in  sketching  objects 
out  of  doors  it  changes  constantly,  and  even  indoors  is  subject  to 
some  fluctuation;  and  then,  in  the  photograph  the  object  is  more 
isolated  from  its  surroundings  and  so  is  less  confusing  to  perceive. 

In  order  to  train  the  sense  of  proportion  as  thoroughly  as  pos- 
sible, the  plates  are  to  be  executed  on  a much  larger  scale  than  the 
examples,  but  at  no  fixed  scale.  Plan  each  drawing  to  be  as  large  as 
possible,  where  no  dimensions  are  given,  but  do  not  allow  any  point 
in  the  drawing  to  approach  nearer  than  one  inch  to  the  border  line. 

34.  Varieties  of  Shading.  In  drawing  in  pen  and  ink,  all 
effects  of  shadow  are  made  by  lines,  and  different  values  are  ob- 
tained by  varying  the  width  of  lines,  or  of  the  spaces  between  the 
lines,  or  by  both.  In  any  case  the  integrity  of  each  line  must  be 
preserved  and  there  can  be  very  little  crossing  or  touching  of  shade 
lines,  as  that  causes  a black  spot  in  the  tone  unless  lines  cross  each 
other  systematically  and  produce  cross  hatching.  With  the  pen- 
cil, however,  owing  to  its  granular  character  one  may  produce  a 
tone  without  any  lines;  a tone  made  tip  of  lines  which  by  touching 
or  overlapping  produce  a soft,  blended  effect,  in  which  the  general 


374 


FREEHAND  DRAWING 


35 


direction  of  the  strokes  is  still  visible,  or  a tone  made  up  of  pure 
lines  as  in  pen  work.  In  general  it  does  not  matter  so  much,  as 
in  pen  drawing,  if  lines  touch  or  overlap.  Indeed,  the  natural 
character  of  the  pencil  line  leads  to  a treatment  which  includes 
both  pure  lines  and  more  or  less  blended  effects. 

35.  Directions  of  Shade  Lines.  It  is  always  a very  impor- 
tant matter  to  decide  what  direction  shade  lines  shall  take.  While 
it  is  impossible  to  give  rules  for  it,  a good  general  principle  is  to 
make  the  direction  of  the  lines  follow  the  contours  of  the  form. 
The  easiest  and  simplest  method  is  to  make  all  the  lines  upright. 
This  method  is  a very  popular  one  with  architects.  The  objec- 
tions to  it  are  monotony  and  a lack  of  expression,  but  it  is  certainly 
a very  safe  method  and  far  preferable  to  one  where  desire  for 
variety  has  been  carried  too  far  and  lines  lead  the  eye  in  a great 
number  of  different  directions  which  contradict  the  general  lines 
of  the  surface  or  form.  A natural  treatment  is  to  adapt  the  direc- 
tion of  lines  to  the  character  of  the  surface  represented;  that  is,  to 
treat  curved  surfaces  with  curving  lines  and  flat  planes  with 
straight  lines,  and  in  general,  lines  may  very  well  follow  either 
the  contours  or  the  surfaces  of  the  form.  I11  that  way  variety  is 
obtained  and  the  direction  of  the  shading  helps  to  express  the  char- 
acter of  the  thing  represented.  This  principle  must,  however,  be 
modified  when  it  leads  to  the  introduction  of  violently  opposing 
sets  of  lines.  Abrupt  transitions  must  be  avoided  and  the  change 
from  one  direction  to  another  must  be  accomplished  gradually. 

Where  a large  surface  is  to  receive  a tone,  the  tone  can  best 
be  made  by  a series  of  rather  short  lines  side  by  side  with  succeed- 
ing series  juxtaposed.  The  lengths 
of  the  lines  in  each  of  the  series  must 
vary  considerably  in  order  that  the 
breaks  in  the  lines  may  not  occur  in 
even  rows,  producing  lines  of  white 
through  the  tone.  (See  Fig.  25.) 

The  crossing  of  one  system  of 
parallel  lines  by  another  system  is 
called  cross  hatching.  This  method 
probably  originated  in  copperplate  engraving,  to  which  it  is  very 
well  adapted,  especially  as  a means  of  modifying  and  deepening 


Fig.  25.  Method  of  Breaking  Lines 
Covering  a Large  Surface. 


375 


36 


FREEHAND  DRAWING 


tones.  It  also  changes  and  breaks  up  the  rather  stringy  texture 
produced  by  a succession  of  long  parallel  lines.  It  has  now  become 
somewhat  obsolete  as  a general  method  for  pen  or  pencil  drawing, 
largely  because  the  result  looks  labored,  for  it  is  always  desirable 
to  produce  effects  more  simply  and  directly,  that  is,  with  one  set 
of  lines  instead  of  two  or  more.  If  the  tone  made  by  one  set  of 
lines  needs  darkening,  it  is  now  more  usual  to  go  over  the  first  tone 
with  another  set  of  lines  in  the  same  direction. 

A great  many  drawings  have  been  made  with  shade  lines  all 
in  a diagonal  direction,  but  this  is  open  to  serious  objection  and 
should  be  avoided.  A diagonal  line  is  always  opposed  to  the  prin- 
ciple of  gravitation,  and  tends  to  render  objects  unstable  and  give 
them  the  appearance  of  tilting.  It  is  often  desirable  to  begin  a 
tone  with  diagonal  lines  which,  however,  should  gradually  be  made 
to  swing  into  either  an  upright  or  horizontal  direction. 


376 


EXAMINATION  PAPER 


FREEHAND  DRAWING 


Materials  Required.  One  Wollff’s  solid  ink  black  pencil;  one  F pencil;  one  HU 
pencil;  two  dozen  sheets  of  paper  (same  as  practice  paper  of  other  courses,  but  to  be  used 
for  examination  sheets  in  this) ; one  red  soft  rubber;  one  medhim  rubber— green  or  red. 
with  wedge  ends ; one  drawing  board ; six  thumb  tacks ; one  box  natural  drawing  models ; 
one  Cross  slate;  one  Cross  pencil;  one-half  dozen  sheets  of  tracing  paper. 

After  the  preliminary  practice  with  straight  lines  and  curves  the  student  may  pro- 
ceed to  execute  Plates  I and  II. 


PLATE  I. 

The  principal  dimensions  in  inches  are  indicated  on  the  model 
plate.  All  dimensions  and  proportions  should  however  be  determined 
by  the  eye  alone.  Measurements  may  be  used  as  a test  after  the 
squares  are  laid  in.  The  figures  on  the  left  should  be  executed  first, 
in  order  to  avoid  rubbing  by  the  hand  and  sleeve. 

Figs.  1,  2,  3,  4,  5 are  motives  from  Egyptian  painted  decoration. 
Figs.  1,  2,  4 and  5 are  all  derived  from  or  suggested  by  patterns  pro- 
duced by  plaiting  or  wearing.  The  borders  of  Fig.  3 are  derived 
from  bundles  of  reeds  bound  together. 

As  all  the  figures  are  large  and  simple,  they  should  be  executed 
with  a rather  wide  line  drawn  with  the  F pencil.  Draw  the  construc- 
tion lines  on  this  and  on  all  other  plates  where  they  are  necessary,  so 
lightly  that  they  can  be  perfectly  erased  without  leaving  any  indenta- 
tion in  the  paper.  After  the  construction  lines  are  drawn  out  in  Figs. 
4 and  5,  strengthen  the  lines  of  the  pattern.  In  erasing,  much  of  the 
pattern  will  be  removed.  This  time  go  over  each  line  with  a single 
stroke  of  the  solid  ink  pencil.  Do  not  turn  the  paper  in  drawing 
diagonal  and  vertical  lines.  They  are  given  especially  to  train  the 
hand  to  execute  such  lines.  By  turning  the  paper  the  exercise  be- 
comes one  of  drawing  horizontal  lines,  which  are  the  least  difficult. 

Fig.  6 is  the  skeleton  of  a very  common  type  of  ornament  con- 
sisting of  curved  lines  radiating  from  a point  at  the  base,  on  either  side 
of  a central  axis. 


379 


3 '5tJ'  I 


PLATE  I. 

Motives  of  Common  Types  of  Ornament. 


FREEHAND  DRAWING 


89 


PLATE  II. 

Fig.  1 is  the  basis  of  a large  class  of  ornament  founded  on  the 
lines  of  organic  growth,  called  scrolls  or  meanders. 

Fig.  2 is  an  Egyptian  border  consisting  of  alternate  flower  and 
bud  forms  of  the  lotus,  the  most  typical  and  universal  of  all  the  Egyp- 
tian decorative  units.  The  outline  of  the  flower  displays  the  Egyp- 
tian feeling  for  subtlety  and  refinement  of  curve.  Observe  how  the 
short  rounded  curve  of  the  base  passes  into  a long  subtle  curve  which 
becomes  almost  straight  and  terminates  in  a short  full  turn  at  the  end. 

Fig.  3 is  a simple  form  of  the  guilloche  (pronounced  gheeyoche), 
a motive  which  first  becomes  common  in  Assyrian  decoration  and  is 
afterward  incorporated  into  all  the  succeeding  styles. 

Fig.  4 is  the  skeleton  of  a border  motive  where  the  units  are  dis- 
posed on  either  side  of  the  long  axis  of  the  border. 

Figs.  5 and  7 are  varieties  of  the  Greek  anthemeum  or  honey- 
suckle pattern,  one  of  the  most  subtle  and  perfect  of  all  ornamental 
forms.  Observe  in  Fig.  5 the  quality  of  the  curves — the  contrast  of 
full  rounded  parts  with  long  curves  almost  straight  which  characterize 
the  Egyptian  lotus.  Note  in  both  examples  that  there  is  a regular 
ratio  of  increase  both  in  the  size  of  the  lobes  and  in  the  spaces  between 
each,  from  the  lowest  one  up  to  the  center.  It  is  invariably  the  ride 
that  each  lobe  shall  be  continued  to  the  base  without  touching  its 
neighbor. 

Fig.  G is  an  Egyptian  “ all-over”  or  repeating  pattern  painted  on 
wall  surfaces.  It  is  made  up  of  continuous  circles  filled  with  lotus 
forms  and  the  intervening  spaces  with  buds. 

PLATE  III. 

This  plate  is  to  contain  nine  outline  drawings  illustrating  Rules 
8,  12,  13,  14,  15,  17,  18,  19,  20.  The  drawings  may  be  made  and  cor- 
rected on  the  slate  and  then  copied  on  to  the  paper  or  they  may  be 
drawn  directly  on  the  paper.  They  may  be  from  the  models  or  from 
simple  geometric  objects  such  as  boxes,  blocks,  cups,  pans,  plates, 
spools,  flower  pots,  bottles,  etc. 

PLATE  IV.* 

These  are  characteristic  forms  of  Greek  vases.  Fig;.  1.  the  Lechv- 

Note.  This  plate  and  all  succeeding  ones  are  to  be  surrounded  by  a border  line, 
drawn  freehand  one  inch  from  the  edge  of  the  paper. 


381 


PlyATE  II. 

Typical  Egyptian,  Assyrian  and  Greek  Motives. 


382 


FREEHAND  DRAWING 


41 


tlios,  was  used  to  hold  oil,  Fig.  2,  the  Kantheros,  is  one  form  of  the 
drinking  cup,  and  Fig.  3,  the  Ilydria,  for  pouring  water. 

The  drawing  of  these  vases  includes  a great  variety  of  beautiful 
curves.  They  are  to  be  executed  entirely  in  outline,  and  both  con- 
tours and  bands  of  ornament  and  the  relative  sizes  of  each  are  to  be 
preserved. 

Calculate  the  heights  so  that  the  bases  shall  each  be  one  inch 
from  above  the  border  line  and  the  upper  point  of  Fig.  3 about  one 
inch  below  the  border  line.  In  sketching  them  in,  first  place  a con- 
struction line  to  represent  the  central  axis.  Across  this,  sketch  the 
outlines  of  the  horizontal  bands  and  then  sketch  the  contours,  follow- 
ing the  general  directions  given  in  Sections  21  and  25.  Remember 
that  lines  are  to  be  drawn  lightly  and  corrections  made  by  new  lines 
and  not  by  erasures.  Use  the  arm  movement  as  much  as  possible  in 
drawing  the  curves.  Before  executing  the  examination  paper,  prac- 
tice drawing  each  vase  entirely  without  corrections  of  the  lines. 

PLATE  V. 

Fig.  1 is  from  the  pavement  in  the  Baptistery  at  Florence  and  is 
in  the  style  called  Tuscan  Romanesque.  The  pointed  acanthus 
leaves  in  the  small  border  to  the  left,  are  identical  in  character  with 
the  Byzantine  acanthus. 

This  drawing  is  to  be  treated  like  a sketch  made  from  the  object. 
After  sketching  in  the  pattern  and  correcting  in  the  usual  way  by 
drawing  new  lines,  erase  superfluous  lines  and  strengthen  the  outlines 
by  lines  made  with  one  stroke.  The  final  outline  should,  however, 
be  loose  and  free  in  character  and  express  the  somewhat  roughened 
edges  of  the  pattern  in  white.  This  does  not  mean  that  the  direction 
of  the  line  must  vary  enough  to  distort  any  shapes.  Observe  that 
most  of  the  shapes  appear  to  be  perfectly  symmetrical  only  their  edges 
seem  slightly  softened  and  broken.  Fill  in  the  background  with  a 
tone  equal  to  the  dark  (D)  of  the  value  scale.  Make  this  tone  by 
upright  lines  nearly  touching  each  other  and  if  the  value  is  too  light 
at  first,  go  over  them  again  by  lines  in  the  same  direction.  If  a back- 
ground line  occasionally  runs  over  the  outline,  it  will  help  to  produce 
the  effect  of  the  original. 

Figs.  2,  3,  4 and  5 comprise  typical  forms  of  Greek  decorated 
mouldings.  The  examples  have  much  the  character  of  a working 


383 


PLATE  IV.  FIG.  1. 

The  Ivechythos. 

Typical  Greek  Vase  Used  to  Hold  Oil. 


PLATE  IV.  FIG.  2. 

The  Kantheros. 

Typical  Greek  Vase  Used  for  a Drinking  Cup. 


PLATE  IV.  FIG.  3. 

The  Hydria. 

Typical  Greek  Vase  Used  far  Pourintr  Water. 


PIRATE)  V.  PIG.  1. 

Pavement  from  the  Baptistery,  Florence. 


FIG.  4 


PI.ATE  V.  FIG>  5; 

Typical  Forms  of  Greek  Decorated  Mouldings. 


48 


FREEHAND  DRAWING 


drawing  and  the  plates  are  to  be  enlarged  copies,  but  instead  of  fol- 
lowing the  character  of  the  light  and  shade  of  the  original,  the  shadows 
are  to  be  executed  by  upright  lines.  (See  Section  37.)  The  darker 
shadows  are  to  be  the  value  of  dark  (D)  of  the  scale,  the  lighter  ones 
the  value  of  middle  (M). 

PLATE  VI. 

Place  these  drawings  so  that  there  will  be  at  least  an  inch  be- 
tween them  and  about  half  an  inch  between  the  border  line  and 
the  top  and  bottom. 

Fig.  1 is  from  a drawing  of  a wrought  iron  grille  in  a church  in 
Prague.  Some  idea  of  the  shape  of  the  pieces  of  iron  is  conveyed  by 
the  occasional  lines  of  shading.  The  pattern  will  be  seen  to  be  dis- 
posed on  radii  dividing  the  circle  into  sixths.  Construct  the  skeleton 
of  the  pattern  shown,  establishing  first  an  ecjuilateral  triangle  and 
the  lines  which  subdivide  its  angles  and  sides.  About  this  draw 
the  inner  line  of  the  circle  and  extend  the  lines  which  subdivide  the 
angles  of  the  triangles,  to  form  the  six  radii  of  the  circle.  Complete 
the  outlines  of  the  pattern  before  drawing  the  shading  lines.  This 
drawing  with  its  lines  and  curves  all  carefully  perfected  represents 
the  kind  of  working  drawing  which  an  architect  might  give  to  an  iron- 
smith  to  work  with,  although  in  a working  drawing,  a section  of  the 
iron  would  be  given  and  each  motive  of  the  design  would  propably  be 
drawn  out  only  once  and  then  as  it  was  repeated  it  would  be  merely 
indicated  by  a line  or  two  sketched  in. 

Fig.  2 is  from  a photograph  of  a wrought  iron  grille  at  Lucca  in 
the  style  of  the  Italian  Renaissance.  The  drawing  to  be  made  from 
this,  the  student  must  consider  to  be  a sketch,  the  sort  of  note  or 
memorandum  he  might  make  were  he  before  the  original. 

The  accompanying  detail  gives  a suggestion  of  the  proper  treat- 
ment. The  general  shape  of  the  whole  outline  should  be  indicated 
and  the  larger  geometric  subdivisions;  the  details  of  two  of  the 
compartments  suggested  by  light  lines  and  those  of  the  remainder 
either  omitted  or  very  slightly  suggested.  Try  to  make  the  drawing 
suggest  the  “hammered”  quality  of  the  iron.  Although  the  curves 
are  all  beautifully  felt,  there  are  slight  variations  in  them  produced 
by  the  hammer,  or  they  are  bent  out  of  shape  by  time,  and  the  thick- 
ness of  the  iron  varies  sometimes  by  intention  and  sometimes  by  acci- 


PI, ATE  VI.  FIG.  1. 
Wrought  Iron  Grille,  Prague. 


PIRATE  VI.  FIG.  2. 
Wroug-ht  Iron  Grille,  Lucca. 


FREEHAND  DRAWING 


51 


dent.  Take  care,  however,  not  to  exaggerate  the  freedom  of  the 
lines  and  do  not  carry  the  variation  so  far  that  curves  are  distorted. 

Make  the  drawing  in  outline  first 
with  a line  which  breaks  occasion- 
ally, with  portions  of  the  line 
omitted.  This  helps  to  indicate 
the  texture  of  the  iron  and  suggests 
its  free  hand-made  character. 

That  part  of  the  background 
which  in  the  photograph  appears 
black  behind  the  iron,  should  be 
filled  in  with  a tone  equal  to  the 
dark  (D)  of  the  value  scale.  It 
should  only  be  placed  behind  the 
two  compartments  which  are  most 
carefully  drawn,  with  perhaps  an 
irregular  patch  of  it  in  the  adjoining 
compartment.  In  making  the  background  use  single  pencil  strokes, 
side  by  side,  wTith  the  solid  ink  pencil,  very  near  together  or  occasion- 
ally touching.  Give  a slight  curve  to  each  stroke.  The  direction 
of  the  lines  may  be  either  upright,  or  they  may  keep  the  leading 
direction  of  the  general  lines  of  the  pattern,  but  they  should  not 
be  stiff  or  mechanical.  If  the  value  is  not  dark  enough  another  set 
of  lines  may  be  made  over  the  first  ones,  keeping  the  same  direction. 
The  only  parts  of  the  ironwork  itself  which  require  shading  are 
those  twisted  pieces  which  mark  the  subdivision,  the  outer  edge, 
and  the  clasp.  For  this  use  a tone  equal  to  the  middle  (M)  of  the 
value  scale.  Avoid  explaining  too  carefully  the  twists  and  use  the 
shading  only  in  the  dark  side.  Use  a few  broken  outlines  on  the 
right  side,  just  enough  to  suggest  it  and  do  not  darken  the  flat  piece  of 
iron  behind  the  twists  except  on  the  shadow  side.  Do  not  count  the 
number  of  twists  but  indicate  them  in  their  proper  size  and  the  effect 
will  be  near  enough  for  this  kind  of  a drawing.  Shade  only  those 
twists  which  are  nearest  the  compartments  which  are  detailed;  from 
them  let  the  detail  gradually  die  away. 

PLATE  VII. 

This  figure  is  a rosette  made  up  of  the  Roman  or  soft  acanthus, 


392 


52 


FREEHAND  DRAWING 


and  the  drawing  has  the  general  character  of  a working  drawing. 
Every  part  is  very  clearly  expressed  in  outline,  slightly  shadowed, 
and  a section  explains  the  exact  contours.  In  drawing  the  outline  of 
the  leaflets,  observe  that  one  edge,  usually  the  upper  is  generally  ex- 
pressed by  a simple  curve  and  the  other  edge  by  a compound  curve, 
the  variation  in  which,  however,  is  slight.  Draw  a circle  first  to  con- 
tain the  outer  edge  of  the  rosette  and  sketch  in  lightly  the  main  rib  or 
central  axis  of  each  leaf.  Then  block  in  the  general  form  of  the  leaves, 
not  showing  the  subdivisions  at  edges.  Next  place  the  eyes — the  small 
elliptical  spots  which  separate  one  lobe  from  another — and  draw  the 
main  ribs  of  each  lobe,  finally  detailing  the  leaflets  in  each  lobe.  In 
shading  use  the  value  dark  (D)  for  the  darkest  values  and  the  middle 
value  (M)  for  the  others,  and  instead  of  producing  a perfectly  blended 
tone  as  in  the  original,  let  the  tone  retain  some  suggestion  of  lines,  the 
general  direction  of  which  should  follow  that  of  the  main  ribs  in  the 
leaves.  In  the  shadow  of  the  rosette  on  the  background,  let  the  lines 
be  upright.  Lines  naturally  show  less  in  very  dark  values  than  in 
lighter  tones,  for  it  is  difficult  to  produce  the  darker  values  without 
going  over  the  lines  with  another  set  and  that  has  a tendency  to  blend 
all  the  lines  into  a general  tone. 

PLATE  VIII. 


Plate  VIII  is  a sculptured  frieze  ornament  introducing  various 
forms  of  the  Roman  or  soft  acanthus.  In  this  as  in  all  scroll  drawing, 
the  skeleton  of  the  pattern  should  be  carefully  drawn,  then  the  leaves 
and  rosettes  disposed  upon  it.  Always  draw  the  big  general  form  of 
the  acanthus,  and  proceed  gradually  to  the  details  as  described  in  the 
directions  for  Plate  VII.  This  like  Plate  VII,  has  the  general  charac- 
ter of  a working  drawing,  only  in  this  case  there  is  no  section.  Use 
the  same  values  and  same  suggestions  for  directions  of  line  as  in 
Plate  VII. 


PLATE  IX. 


This  plate  is  an  example  of  the  Byzantine  acanthus  on  a fragment 
in  the  Capitoline  Museum.  In  drawing  this,  place  the  central  axis  or 
main  rib  of  the  leaf  first,  then  establish  the  position  of  the  eyes — the 
egg-shaped  cuts  which  separate  the  lobes.  The  general  contour  of 
the  lobes  and  their  main  ribs  should  next  be  blocked  in  before  the 
final  disposition  of  the  points  or  leaflets  is  determined. 


394 


Section  Througii  Center. 

PLATE  VII. 

Acanthus  Rosette. 


PLATE  IX. 

This  is  also  to  be  drawn  as  Fig-.  1,  Plate  X. 

Byzantine  Acanthus,  from  a fragment  in  the  Capitoline  Museum. 


56 


FREEHAND  DRAWING 


The  drawing  of  this  plate  is  to  be  enlarged  to  about  ten  inches  in 
height  and  well  placed  on  the  sheet  with  the  center  of  the  drawing 
coinciding  with  the  center  of  the  plate.  This  drawing  is  to  be  made 
by  the  use  of  two  values  only,  with  white,  and  the  student  may  select 
his  own  values.  The  object  is  to  select  the  most  important 
features  and  to  omit  as  much  as  possible.  It  would  be  well  for 
the  student  to  first  try  to  see  how  much  he  can  express  with  one 
value  and  white.  The  values  are  to  be  obtained  by  upright  lines. 
Outlines  are  to  be  omitted  as  far  as  possible  in  the  finished  sketch 
and  forms  are  to  be  expressed  by  the  shapes  of  the  masses  of 
shadow.  Where  only  two  values  and  white  are  to  be  used,  it  is 
desirable  to  leave  as  much  white  as  possible  and  not  allow  the 
shadow  values  to  run  too  near  to  black  as  that  produces  too  harsh  a 
contrast  with  the  white.  On  the  other  hand,  if  the  shadow  values  are 
too  high  in  the  scale,  that  is  too  near  white,  the  drawing  becomes  weak 
and  washed  out  in  effect.  As  this  drawing  is  to  be  large  in  scale,  it 
should  be  made  with  the  solid  ink  pencil  and  with  wide  pencil  strokes. 
After  the  outline  has  been  sketched  in,  the  shading  or  “ rendering” 
may  be  studied,  first  on  tracing  paper  over  the  drawing.  There 
should  be  no  attempt  at  rendering  the  background  in  this  drawing. 

PLATE  X. 

Figs.  1 and  2 are  to  be  placed  on  this  plate,  but  Fig.  1 is  to  be 
rendered  this  time  as  near  to  the  true  values  as  it  is  possible  to  go 
by  using  four  values  and  white  in  shading.  The  pencil  lines  should 
be  blended  together  somewhat,  but  the  general  direction  of  the  shad- 
ing should  follow  the  central  axis  of  the  lobe§.  Only  the  leaf  itself 
is  to  be  drawn  and  the  background  value  should  be  allowed  to  break 
in  an  irregular  line  about  the  leaf.  It  shoukl  not  be  carried  out  to  an 
edge  which  would  represent  the  shape  of  the  entire  fragment  of  stone 
on  which  the  leaf  is  carved.  In  studying  the  shapes  of  the  different 
shadows  it  is  well  at  first  to  exaggerate  somewhat  and  give  each  value 
a clean,  definite  shape  even  if  the  edges  appear  somewhat  indefinite 
in  the  original.  At  the  last  those  edges  which  are  blurred  may  be 
blended  together. 

Fig.  2 is  a Byzantine  capital  from  the  church  of  San  Vitale,  at 
Ravenna.  This  is  to  be  drawn  so  that  the  lines  of  the  column  shall 
fade  off  gradually  into  nothing  and  end  in  a broken  edge  instead  of 


FREEHAND  DRAWING 


57 


stopping  on  a horizontal  line  as  in  the  original.  The  top  of  the  draw- 
ing above  the  great  cushion  which  rests  on  the  capital  proper  should 
also  fade  off  into  nothing  and  with  a broken  line  instead  of  the  hori- 
zontal straight  line.  A small  broken  area  of  the  background  value 
should  be  placed  either  side  of  the  capital.  In  drawing  an  object  like 
this  which  is  full  of  small  detail  there  is  danger  of  losing  the  larger 
qualities  of  solidity  and  roundness  by  insisting  too  much  upon  the 
small  parts  and  there  is  also  danger  of  making  the  drawing  too  spotty. 
It  is  a good  principle  to  decide  at  first  that  the  detail  is  to  be  expressed 
either  in  the  shadow  or  in  the  light,  but  not  equally  in  both.  This 
principle  is  based  on  one  of  the  facts  of  vision,  for  in  looking  at  an 
object  one  sees  only  a comparatively  small  amount  of  detail;  what 
falls  on  either  side  of  the  spot  on  which  the  eye  is  focused  appears 
blurred  and  indistinct.  In  an  object  of  this  kind  whose  section  is 
circular,  one  can  best  express  the  shape  by  concentrating  the  study 
of  detail  at  the  point  where  the  light  leaves  off  and  shadow  begins, 
representing  less  and  less  detail  as  the  object  turns  away  from  the 
spectator.  In  this  drawing,  however,  there  may  be  more  detail  ex- 
pressed in  the  shadow  than  in  the  light,  but  remember  that  outlines 
of  objects  in  shadow  lose  their  sharpness  and  become  softened.  Do 
not  attempt  to  show  all  the  grooves  in  the  parts  in  shadow;  indicate 
one  or  two  principal  ones  and  indicate  more  and  more  detail  as  the 
leaves  approach  the  point  where  the  light  begins.  There  the  richness 
of  detail  may  be  fully  represented,  but  as  the  forms  pass  into  the  light, 
omit  more  and  more  detail.  Again  observe  that  any  small  plane  of 
shadow  surrounded  by  intense  light,  if  examined  in  detail,  appears 
darker  by  contrast,  but  if  represented  as  dark  as  it  appears  it  becomes 
spotty  and  cut  of  value.  If  observed  in  relation  to  the  whole 
object  its  real  value  will  be  seen  to  be  lighter  than  it  appears  when 
examined  by  itself.  Use  whit3  and  four  values  to  be  determined  by 
the  student.  Guard  against  too  strong  contrasts  of  values  within  the 
shadow  as  it  cuts  it  up  and  destroys  its  unity,  and  in  every  drawing 
made,  show  clearly  just  which  is  the  shadow  side  and  which  is  the 
light.  That  is,  do  not  place  so  many  shadow  values  within  the  light 
that  it  destroys  it,  and  do  not  invade  shadows  with  too  many  lights 
and  reflected  lights.  Note  that  it  is  characteristic  of  the  Byzantine 
acanthus  to  have  the  points  of  every  tine  or  lobe  touch  something; 
no  points  are  left  free,  but  observe  also  that  the  points  have  some  sub- 


309 


58 


FREEHAND  DRAWING 


stance  and  width  at  the  place  they  touch  and  must  not  be  represented 
by  a mere  thread  of  light.  It  would  be  a mistake  to  introduce  much 
variety  of  direction  in  the  lines  in  this  drawing,  especially  in  the 
shadows,  as  it  would  “ break  it  up  ” too  much.  The  concave  line  of 
the  contour  of  the  capital  may  well  determine  the  dominant  direction 
of  the  lines  which  should  not  be  very  distinct  as  lines,  but  should  blend 
considerably  into  general  tones.  W herever  a plane  of  shadow  stops 
with  a clean  sharp  edge  the  drawing  must  correspond,  for  its  interest 
and  expressiveness  depend  upon  its  power  to  suggest  differences  in 
surface — those  surfaces  which  flow  gradually  into  one  another  as  well 
as  those  in  which  the  transitions  are  sharp  and  abrupt. 

The  student  should  be  very  scrupulous  about  using  only  the 
values  of  the  scale,  and  in  the  lower  left  corner  of  each  sheet  he  should 
place  within  half-inch  squares  examples  of  each  value  used  on  the 
drawing  with  its  name  and  symbol  indicated. 

PLATE  XI. 

This  capital,  of  the  Roman  Corinthian  order,  is  in  the  Museum  of 
the  Baths  of  Diocletian  in  Rome. 

The  foliated  portions  consist  of  olive  acanthus,  and  the  student 
should  carefully  study  the  differences  between  this  and  the  soft  acan- 
thus. It  will  be  noted  that  the  greatest  difference  is  in  the  subdivi- 
sion of  the  edges  into  leaflets.  In  the  soft  acanthus  there  is  always  a 
strong  contrast  of  large  and  small  leaflets  and  the  lobes  overlap  each 
other,  producing  a full  rich  effect  and  the  general  appearance  is  more 
like  that  of  a natural  leaf.  In  the  olive  acanthus  the  leaflets  in  one 
lobe  differ  slightly  from  each  other  in  size,  are  narrower,  and  bounded 
by  simple  curves  on  either  side,  where  the  leaflet  of  the  soft  acanthus 
has  the  compound  curve  on  one  side. 

The  student  may  use  as  many  values  as  he  thinks  necessary,  but 
he  should  be  conscientious  in  keeping  his  values  in  their  scale  relations 
and  should  place  an  example  of  each  value  used,  with  its  name  in  one 
corner  of  the  drawing. 

To  make  a satisfactory  drawing  of  a form  so  full  of  intricate 
detail  as  this  is  difficult,  as  there  is  a great  temptation  to  put  in  all  one 
sees.  The  general  instructions  for  drawing  Plate  VII  are  equally 
applicable  here.  The  student  should  remember  that  a drawing  is  an 
explanation,  but  an  explanation  which  can  take  much  for  granted, 


400 


PLATE  X.  FIG.  2. 

Byzantine  Capital,  from  the  Church  of  San  Vitale  Ravenna. 


PLATE  XI. 

Roman  Corinthian  Capital,  from  the  Baths  of  Diocletian. 


PLATE  XII. 

Italian  Renaissance  Pilaster. 


62 


FREEHAND  DRAWING 


For  instance,  if  the  carved  ornament  on  the  mouldings  or  at  the  top 
of  the  capital  are  expressed  where  they  receive  full  light,  they  must 
become  more  and  more  vague  suggestions  and  finally  disappear  in 
the  strong  shadows;  so  the  division  line  between  the  two  mouldings 
of  the  abacus  may  be  omitted  in  shadow  and  the  mind  will  fill  in 
what  the  eye  does  not  see.  One  could  go  farther  and  express  the  detail 
only  for  a short  space,  letting  it  gradually  die  away  into  light  or  be 
merely  indicated  by  a line  or  two,  and  still  the  explanation  would  be 
sufficient  and  far  less  fatiguing  to  the  eye  than  literal  insistence  on 
every  detail  for  the  entire  length.  It  is  an  excellent  plan  to  look  at 
the  original,  whether  a photograph  or  the  real  object,  with  half  closed 
eyes.  This  helps  decidedly  to  separate  the  light  masses  from  the 
darks  and  shows  how  much  that  is  in  shadow  may  be  omitted. 

The  smaller  lobes  on  the  olive  acanthus  have  no  main  ribs  and 
lines  are  carried  from  the  intersection  of  each  leaf  toward  the  base, 
the  section  of  the  leaflet  being  concave.  The  section  of  the  leaflets 
on  the  soft  acanthus  is  more  V-shaped. 

PLATE  XII. 

This  is  a portion  of  a pilaster  decoration  in  the  Italian  Renais- 
sance style.  The  acanthus  is  of  the  soft  Roman  type,  but  much  more 
thin  and  delicate  with  the  eyes  cut  back  almost  to  the  main  ribs  and  a 
space  cut  out  between  each  lobe  so  there  is  rarely  any  overlapping 
of  lobes.  Lay  out  construction  lines  for  the  scrolls,  block  in  all  forms 
correctly/  detailing  little  by  little,  so  carrying  the  whole  drawing  along 
to  the  same  degree  of  finish 


404 


.Me-in.  BvildirvR 

ARM°VR  INSTITVTE 

op  TECHNOLOGY 


A STUDY  IN  PEN  AND  INK  RENDERING. 

(F°r  a different  treatment  of  the  same  building , see  page  248.) 


RENDERING  IN  PEN  AND  INK, 


learn  engraving  on  wood  in  a f< 
ink- rendering  difficulties  are  to 


To  render  in  pen  and  ink  a 
large  and  important  drawing  is 
no  small  accomplishment.  Usu- 
ally years  of  experience  are  nec- 
essary before  one  can  sucess- 
fully  undertake  such  drawings. 
Now  and  then  a student  is  to  be 
found  having  talent  to  the  ex- 
tent  that  the  attainment  of  this 
skill  seems  a very  easy  matter, 
but  in  general  this  talent  is  com- 
paratively rare.  N inety-five  out 
of  every  hundred  have  a long 
task  ahead  before  success  is  pos- 
sible. This  difficulty  of  attain- 
ment, however,  makes  the  ac- 
complishment all  the  more  val- 
uable. No  one  would  expect  to 
brief  lessons,  and  yet  in  pen  and 
met  not  unlike  those  connected 


with  engraving. 

But  there  are  many  things  concerning  pen  and  ink  work 
which  can  be  readily  learned ; they  are  worth  the  trouble  and  the 
labor  expended,  and  may  prove  useful.  A consideration  of  these 
will,  in  any  case,  introduce  the  art  and  serve  also  as  a good  founda- 
tion for  further  pursuit  of  the  subject  if  desired. 

It  is  the  purpose  of  this  paper  to  seek  the  most  modest  of 
results,  which  may  be  set  forth  thus, — the  rendering  of  a small 
building  at  a small  scale  in  the  very  simplest  manner,  with  few 
or  no  accessories. 

Kind  of  Drawing.  There  are  three  ways  in  which  a sketch 
may  be  rendered,  viz:  with  pen,  pencil,  or  brush.  Pen  rendering 
will  be  considered  first,  and  later  additional  notes  will  be  made  as 
to  pencil  work.  Rendering  with  the  brush  is  another  line  of  work, 


407 


4 


RENDERING 


but  much  that  may  be  advised  in  regard  to  pen  rendering  would 
also  apply  to  brush  work. 

MATERIALS. 

Pens.  The  tendency  of  beginners  is  to  use  too  fine  a pen. 

It  must  be  remembered  that  many  pen  drawings  are  reproductions 

much  smaller  than  the  originals,  and  consequently  the  lines  appear 

much  finer  than  in  the  drawing  itself.  There  are  two  pens  that  can 

be  recommended,  shown  herewith.  Years  of  experience  prove 

them  to  be  perfectly  satisfactory.  Occasionally  a finer  pen  is 

needed,  such  as  Gillott  No.  303.  The  Esterbrook  No.  14,  a larger 

pen,  is  necessary  in  making  the  blacker  portions  of  a drawing.  The 

Gillott  404  is  to  be  used  for  general  work  in  the  same  drawing. 

Ink  is  not  of  as 
ESTERBROOK  BANK  . . 

pen,  no.  14.  much  importance 

as  pens.  The  va- 

gillott no. 404.  rious  prepared 

India  inks  put  up 

in  bottles  are  all  that  can  be  desired.  They  are  more  convenient 

than  ink  that  must  be  rubbed  up,  and  they  have  the  advantage 

of  always  being  properly  black.  Some  ordinary  writing  inks 

• serve  the  purpose  very  well  if  reproduction  is  not  an  object,  but 

if  reproduction  is  desired,  India  ink,  being  black,  is  preferred. 

Paper.  The  very  best  surface  is  a hard  Bristol  board.  The 
softer  kinds  of  Bristol  boards  should  be  avoided,  as  they  will  not 
stand  erasure.  Most  of  the  drawing  papers  do  very  well.  What- 
man’s hot  pressed  paper  is  very  satisfactory.  An  excellent  draw- 
ing surface  is  obtained  by  mounting  a smooth  paper  on  cardboard, 
thus  obtaining  a level  surface  that  will  not  spring  up  with  each 
pressure  of  the  pen.  This  is  equivalent  to  a Bristol  board. 
However,  the  size  of  Bristol  board  is  limited  and  frequently  draw- 
ings must  be  much  larger,  in  which  case  the  mounted  paper  is  a 
necessity. 

LINE  WORK. 

Quality  of  Line.  Too  much  stress  cannot  be  laid  on  the  im- 
portance of  a good  line,  however  insignificant  it  may  seem.  Care 
in  each  individual  line  is  absolutely  necessary  for  good  work.  A line 


408 


RENDERING 


5 


GOOD  QUALITY  OF  LINE. 


that  is  stiff  and  Laid,  feeble,  scratchy  or  broken,  will  not  do.  Such 
work  will  ruin  a drawing  that  in  other  respects  may  be  excel- 
lent. The  accompanying  illustration  by  one  of  the  students  of  the 
Massachusetts  Institute  of  Technology  is  an  example  of  excellent 
quality  of  line.  Each  line,  even  to  the  very  smallest,  has  grace  and 
beauty.  By  a very  few,  the  ability  to  make  such  lines  is  speedily  ac- 
quired— but  by  a few  only — others  may  attain  it  by  careful  practice. 

Every  line  of  a drawing-^the  outline  of  the  building  and 
each  line  of  the  rendering,  even  to  the  very  shortest  must  be  done 
feelingly,  gracefully,  positively.  Usually  a 


WMtott  «"  Pin#  lit 

(ii! 


Ilk 


miu/ju 


slight  curve  is  advisable  and  if  long  lines  are 


I 


end. 


used,  a quaver  or  tremble  adds  much  to  the 
result.  Each  line  of  a shadow  should  have 
a slight  pressure  of  the  pen  at  the  lower 
This  produces  a dark  edge  in  the  group  of  lines  that 


409 


6 


RENDERING 


make  the  shadows,  giving  definiteness  to  the  shadow  and  contrast 
to  the  white  light  below  it. 

Method.  The  combination  of  individual  lines  produces  what 
we  may  term  a method.  The  individual  line  may  be  good  but 
the  combining  may  be  unfortunate.  In  making  a wash  drawing 
no  thought  is  necessary  concerning  the  direction  of  the  wash,  but 
in  using  lines  at  once  the  query  arises  as  to  what  direction  they 


shall  take.  A method  is  something  one  must  grow  into  from  a 
small,  simple  beginning.  The  accompanying  illustration,  the 
work  of  another  Massachusetts  Institute  of  Technology  student,  is 
an  example  of  rare  skill  in  method  quickly  acquired.  There  is  an 
utter  absence  of  anything  rigid  or  mechanical  in  the  wThole.  Ob- 
serve how  softly  the  edges  of  the  drawing  merge  in-to  the  white  of 
the  paper.  The  vigor  of  the  drawing  is  gathered  in  the  dormer 
itself. 


410 


RENDERING 


7 


Vertical  Lines.  The 

simplest  method  is  ob- 
tained by  the  use  of  the 
vertical  line.  Some  draw- 
ings can  be  made  entirely 
by  this  means.  See  Fig. 

3,  every  line  of  which  is 
vertical.  This  illustrates 
the  value  of  a good  indi- 
vidual line.  It  will  be  d* 
observed  that  although  ver- 

o 

tical,  these  lines  are  not 
severely  straight  and  stiff, 
they  tremble  a little,  or 
have  a slight  suggestion 

o oo 

of  a curve.  In  the  sliad- 

i*  Ate,  \ 


Fig.  4. 

FREE  LINE  METHOD. 


Fig.  3. 

VERTICAL  LINE  METHOD. 

ow  at  the  bottom  of  the 
drawing  each  line  is  em- 
phasized  at  the  top  by  a 
slight  pressure,  and  made 
thin  at  the  lower  end  in 

' “ sA  . * 

order  to  soften  off  the 
edges  of  the  drawing  as  a 
whole. 

Free  Lines.  Eig.  4 
shows  another  method. 
The  vertical  line  is  dis- 
carded and  the  freest  pos- 
sible line  is  used.  No 
one  direction  is  followed, 
but  the  lines  go  in  any 
or  all  directions.  Which 


411 


8 


BEN  DERING 


is  the  better  method  ? The  answer  doubtless  must  be  that  the  free 
method  is  the  least  conspicuous.  It  is  better  adapted  for  general 
use,  in  the  showing  of  various  surfaces  and  textures. 

VARIOUS  EXAMPLES  OF  METHODS. 


Short,  broken  line,  resulting  in 
a spotty  effect;  a fault  common 
with  beginners.  The  white  spaces 
between  the  ends  of  the  lines  are 
very  conspicuous. 


Short  lines,  individually  they 
may  be  very  good,  as  they  curve 
freely,  but  the  combination  is 
fussy  and  finnicky. 


The  opposite  in  character  to  A. 
Long,  unbroken  lines,  but  so  se- 
verely straight  as  to  be  hard  and 
dry  in  general  appearance. 


Direction  of  line  not  bad,  but  is 
rather  too  coarse  to  be  agreeable. 
Wide  spacing  of  lines  on  light  por- 
tions add  to  the  coarse  result. 


These  illustrate  four  bad  methods.  A has  the  least  merit,  the 
others  approach  to  a fair  quality.  In  E an  effort  is  made  to  avoid 
all  the  faults  shown  in  the  others — the  short  or  severely  straight 
line,  the  over  labor  combination  of  C,  and  the  coarse  line  of  D. 


LIGHT  AND  SHADE. 

Values.  If  several  lines  are  drawn  parallel  and  quite  close 
together,  but  not  touching,  a gray,  or  half-tone  value  is  the  result. 


412 


RENDERING 


9 


Lines  drawn  so  close  together  that  the  ink  of  one  runs  into  that  of 
the  other,  with  little  or  no  white  space  between,  give  a black 


value.  The  white  of  the  paper  untouched  by  the  pen  gives  a 
white  value.  Fig.  5 shows  only  two  values — black  and  white; 


Fig.  6 also  has  two, — gray 
and  white;  Fig.  7 has  the 
three, — black,  gray  and  white. 
The  first  is  harsh,  the  second 
is  pale,  and  the  third  seems 
most  satisfactory. 

This  is  a safe  rule  to  follow 
— get  into  every  pen  drawing, 
black,  gray  and  white.  Usu- 
ally, in  early  attempts,  there 
is  a tendency  to  omit  the  black. 
Look  for  the  place  in  the 


Fig.  6. 

GRAY  AND  WHITE. 


Fig.  5. 

BLACK  AND  WHITE. 


Fig.  7. 

BLACK,  GRAY  AND  WHITE. 


413 


10 


RENDERING 


drawing  where  you  can  locate  this  black;  you  are  not  likely  to  get 
too  much  of  it.  Let  the  half  tone  or  gray  be  rather  light,  mid- 
way in  strength  between  white  and  black.  A heavy  half  tone  is 


Fig.  8, 

ONE  SIDE  IN  SHADE. 

a dangerous  value.  The  black  may  often  grade  off  into  the  gray, 
or  there  may  be  distinct  fields  or  areas  of  each  value. 

Lighting.  The  first  thing  to  consider  in  the  rendering  of  an 
architectural  subject  is  the  choosing  of  the  direction  of  light. 
Sometimes  when  the  building  is  turned  well  to  the  front,  showing 

O ' o 


Fig.  9. 

ALL  IN  LIGHT. 

a sharp  return  of  the  end,  it  may  be  best  to  put  that  side  in  shade, 
Fig.  8,  but  it  is  not  necessary.  Values  may  be  obtained  by  other 
means  such  as  by  shadows,  or  color  of  material.  It  is  not 
wise  to  attempt  a heavy  rendering  in  pen  work.  Usually  it  is  safer 


RENDERING 


11 


to  keep  both  sides  of  the  building  in  light  as  shown  in  two  of  these 
sketches,  Figs.  9 and  10. 


Fig.  10. 

ALL  IN  LIGHT  WITH  HALF-TONE  VALUE  TO  ROOF. 


Color  of  riaterial.  One  of  the  means  by  wThich  values  may  be 
introduced  into  a rendering,  is  by  considering  the  color  of  the  ma- 
terial of  which  the  building  is  constructed. 

O 


Fig.  11. 

HALF-TONE  WALLS. 


In  this  example,  Fig.  11,  we  may  first  use  the  brick  walls  as 
a place  to  locate  a gray  value.  In  the  second  example,  Fig.  12, 
the  roof  is  used  for  the  same  value.  For  the  very  dark  or  black 
value  we  must  depend  on  the  shadows.  Neither  one  of  these  draw- 


415 


12 


RENDERING 


ings  is  wholly  satisfactory.-  In  the  first,  the  roof,  and  in  the  other, 
the  walls,  seem  too  glaringly  white.  For  that  reason  it  is  not 
always  best  to  use  the  material  color  so  broadly.  To  give  color  to 


HALF-TONE  ROOF. 


both  walls  and  roof  would  destroy  the  white  value,  and  the  white 
value  must  not  be  lost.  Fig.  13  shows  an  attempt  at  a compro- 
mise. 

Shadows  Only.  The  simplest  means  for  obtaining  values  is 


416 


RENDERING 


13 


by  the  use  of  shadows.  Sometimes  the  shadows  alone  will  com- 
plete a drawing  in  a very  satisfactory  manner,  as  in  Fig.  14. 
Some  of  the  shadows  may  be  made  gray,  and  others  black  or  nearly 
so,  in  order  to  get  the  needed  variety  in 
values. 

A building  like  that  shown  in  Fig.  15, 

The  Alden  House,  is  not  favorable  to 
shadows  only.  It  has  no  porch  or  other 
projection  sufficiently  large  to  cast  a 
strong  shadow.  In  such  a case  a little 
accessory  helps  one  out  of  the  difficulty, 
and  a little  rendering  of  the  material  gives 
needed  half  tone.  Otherwise  the  draw- 
ing would  be  too  white. 

Principality  or  Accent.  4\re  now  enter 
into  a matter  of  composition.  One  sim- 
ple rule  will  be  given  and  there  is  none 
more  useful.  Let  there  be  one  place  in 
the  drawing  where  a strong  accent  of  black  shall  exist.  It  may  be 
one  black,  or  it  may  be  a group  of  them.  This  accent  will  be 
found  in  nearly  every  illustration  in  this  paper.  It  is  usually  best  to 


get  the  accent  in  the  building  itself,  by  the  aid  of  some  large  shad- 
ow perhaps,  but  when  there  is  no  chance  for  this  it  may  be  neces- 
sary to  get  it  in  an  accessory  such  as  foliage.  This  is  shown 
in  Fig.  16,  a drawing  of  a barn.  In  connection  with  this 
black  accent  let  there  be  a large  white  area  if  possible.  A princi- 


SHADOWS  ONLY. 


417 


Por-t-EvJ  £>e//i/N,  a o B'/^aaioy 


RENDERING 


15 


pal  white,  as  well  as  a principal  black  is  thus  obtained.  Most 
drawings  permit  the  dark  accent  and  the  light  area  also. 

Fig.  17  is  rendered  to  a greater  extent  than  should  be  at- 
tempted  by  the  student  in  this  course,  but  it  may  be  helpful  to 
call  attention  to  some  things  in  its  composition. 


The  location  of  the  dark  accent  is  apparent  in  the  trees  at  the 
left.  The  other  blacks,  the  trees  in  front  of  the  building  and 
those  down  at  the  extreme  right,  simply  repeat  in  diminishing 
force  and  size,  this  first  dark  accent.  The  light  area  of  the  draw- 
ing is  as  distinctly  shown  as  the  dark  accent;  in  fact  this  large 
light  is  the  feature  of  this  rendering.  The  light  brick  rendering 
of  the  gable  is  necessary  to  confine  the  light  a little  more  surely 
to  the  important  portion  of  the  wall.  Also,  if  this  light  rendering 
were  omitted  the  building  would  appear  unpleasantly  white. 

The  half  tone  of  the  roof  is  necessary  to  give  a soft  contrast 
to  the  light  wall  surface.  The  sky  has  its  use.  Cover  it  up,  and 
see  how  the  whole  subject  slumps  downward. 

Last,  but  not  least,  observe  that  the  corners  of  the  drawing 
are  kept  free  from  rendering.  This  is  usually  safe.  Let  the 
rendering  of  every  sort  gather  about  the  central  object.  The  cor- 
ners of  a drawing  may  then  be  left  to  take  care  of  themselves. 

PENCIL  WORK. 

A pencil  is  a quicker  medium  for  the  rendering  of  a sketch 
than  a pen.  A pencil  sketch  may  be  made  directly  on  a sheet  of 
drawing  paper,  and  completed  on  that  same  sheet.  But  it  is 
neater  to  first  draw  the  perspective  on  smooth  white  paper,  then 
place  Alba  tracing  paper  over  this  outline,  and  trace  and  render. 
By  this  means  all  construction  lines  in  the  layout  can  be  omitted, 


419 


16 


RENDERING 


and  the  sunny  edge  of  projections  can  be  left  out,  thus  adding 
greatly  to  the  brightness  of  the  drawing. 

Use  a soft  pencil  for  rendering,  a BB  or  softer.  If  the  draw- 
ing is  to  be  much  handled,  spray  it  with  fixatif.  Trim  the  sketch, 
lightly  gum  the  corners,  and  lay  on  white  card  with  good  margin. 

SUMMARY. 

The  following  summary  of  advice  for  the  rendering  of  work 
generally,  with  pen  or  pencil  may  be  found  helpful. 

1.  Consider  the  direction  of  the  light. 

2.  Discover  in  the  outline  before  you.  the  opportunity  for  a 
leading;  dark  accent. 

3.  Look  out  also  for  the  location  of  a large  light  area. 

4.  Put  in  shadows. 

5.  Get  at  least  three  distinct  values;  black,  gray  and  white. 

6.  Consider  the  color  of  roof  or  the  wall,  and  if  necessary 
use  one  of  them  or  portions  of  each  for  a gray  value. 

7.  Use  a very  free  method. 

8.  Keep  rendering  out  of  the  corners  of  the  drawing. 


1 


AN  APPLICATION  OF  PEN  AND  INK  RENDERING  TO  THE  CONVENTIONAL  METHOD  OF  INDICATING 
PATHS,  SHRUBBERY,  TREES,  TERRACES,  ETC.,  IN  PLAN. 

This  is  usually  done  in  washes. 

( See  also  t>ages  1 8 and  45 3) . 


EXAMINATION  PAPER 


EXA'lf  NATION  PLATES. 

With  this  Instruction  Paper  are  sent  three  sets  of 
outline  plates;  one  set  for  practice  with  pencil,  one  set 
for  practice  with  ink  and  the  third  set  (on  better  paper) 
to  be  rendered  in  ink  and  sent  to  the  School  for  correc- 
tion and  criticism.  The  practice  work  need  not  be  sent 
to  the  School. 

Should  the  ink  not  flow  well,  rub  the  whole  plate 
lightly  with  a soft  eraser,  or  rub  over  it  a little  powdered 
chalk.  Before  beginning  to  render  the  drawing,  dust  off 
any  loose  chalk  remaining  on  the  paper. 

Plates  I to  VI  inclusive  constitute  the  examination 
for  this  instruction  paper.  The  student’s  name  should 
be  lettered  in  the  lower  right-hand  corner  in  a manner 
similar  to  that  shown  in  the  illustrations  of  the  Instruc- 
tion Paper. 


RENDERING 


19 


EXAMINATION  PLATES. 

Before  attempting  to  render  the  drawings  in  ink,  the  student 
is  advised  to  practice  both  with  pencil  and  ink,  using  the  practice 
plates  provided  for  the  purpose. 

PLATE  I. 

In  order  to  get  quickly  into  the  practice,  the  student  will  he 
asked  to  make  a copy  of  this  rendering,  Fig.  A.  Do  not  try  to 
copy  too  exactly,  but  use  the  same  freedom. 

Observe  that  the  dark  accent  is  obtained  by  the  large  shadow 
and  the  end  of  the  long  shadow  just  over  it.  The  dark  rendering 
in  the  window  is  brought  into  the  group  also. 

Having  thus  formed  the  accent,  it  is  best  that  the  shadow 
under  the  hood  in  the  roof  should  be  made  rather  light,  lest  it 
come  into  competition  with  the  porch  shadow.  If  the  student 
prefers  he  may  make  it  a trifle  darker  than  here  shown. 

A little  clapboard  rendering  is  put  in  on  the  left,  to  make 
still  more  evident  the  large  light,  which  occurs  mainly  on  the  roof 
but  at  the  same  time  takes  in  other  white  spaces  at  that  end  of  the 
drawing. 

PLATE  II. 

Tliis  subject  introduces  a roof  rendering,  also  a simple  treat- 
ment of  windows  and  blinds.  Here  the  roof  serves  as  a half-tone 
value.  The  shadow  of  the  eaves  and  some  of  the  blinds  are  the 
black  values.  To  get  the  dark  accent,  the  nearest  blinds  and  the 
near  portion  of  the  shadow  on  the  eaves  are  made  very  dark. 

The  shadow  under  the  porch  shows  how  safely  much  of  the 
detail  of  the  door  itself  may  be  omitted  and  not  be  missed.  A broad 
treatment  is  better  than  a fussy  one.  Observe  that  the  roof  lines 
are  made  as  free  as  possible,  avoiding  a straight,  wiry  line. 

After  copying  this  plate  original  work  may  be  attempted. 

PLATES  III  AND  IV. 

Make  the  shadows  only  for  the  first  rendering,  Plate  III,  just 
as  shown  in  this  value  scheme,  Fig.  C.  Then  make  a second 
drawing  of  the  same,  Plate  IV,  and  give  a half  tone  to  the  front 
area  of  the  roof,  and  to  the  end  of  the  roof  a darker  value,  as 
shown  in  suggestion  in  upper  corner.  Finally  on  this  second 


425 


PLATE 


OUTLINE  DRAWING  READY  FOR  RENDERING. 

All  lines  should  be  very  light  so  as  not  to  show  through  rendering. 


finished  drawing. 


PLATE 


< 


Fig.  B.  (For  Plate  II.) 


^LATE 3 


TWO  DIFFERENT  TREATMENTS  OF  SAME  SUBJECT, 
(See  opposite  page.) 


\3  3XV1J 


EENDEPJNG 


21 


drawing,  put  a small  amount  of  rendering  on  the  wall  at  the  distant 
right,  in  the  same  manner  as  on  Plate  II.  This  will  give  a large 
white  light  on  the  walls  nearest  the  observer.  The  long  shadows 
under  the  eaves  should  be  darkest  at  the  corner  nearest  the  observer 
and  gradually  lighten  up  as  it  approaches  either  end. 


PLATE  V. 

Put  in  the  shadows  first.  Get  the  nearest  shadows  very  dark; 
then  give  a half-tone  rendering  to  the  whole  of  the  brick-wall  sur- 
face. Do  not  ink  in  the  lines  at  the  edges  of  the  brick  walls.  Let 

O 


Fig.  D.  (For  Plate  V.) 

your  rendering  make  the  edge  as  shown  in  Fig.  18.  An  outline  in 
such  a place  produces  a mechanical  looking  rendering,  as  is  seen  in 
the  illustration.  Outlining  is  absolutely  necessary  where  there 


433 


REN  DEEDS  G 


99 


is  no  rendering,  but  in  connection  with  it,  omit  the  outline,  if 

PLATE  VI. 

The  doorway  shadow  selects  for  itself  the  honor  of  being  the 
leading  accent;  the  shadows  at  left  and  right  simply  repeat  it  in  a 
small  way.  The  roof  affords  an  opportunity  for  half-tone.  The 


Fig.  E.  (For  Plate  VI.) 


grass,  which  may  be  rendered  as  illustrated  in  the  two  preceding 
examples,  gives  also  an  additional  half-tone  value.  To  retain  or 
produce  a large  light  area,  the  stone  jointing  should  be  omitted  on 
the  upper  portion  of  the  wall,  as  indicated  in  the  scheme.  The 
roof  may  be  rendered  in  a free  line  method,  as  shown  in  the  sketch. 
With  a good  quality  of  line,  and  a free,  vigorous  method,  this  draw- 
ing will  be  a brilliant  one,  as  its  composition  of  values  is  favorable. 


434 


PLATE  fl' 


24 


RENDERING 


This  ends  the  practice.  Only  a beginning  has  been  made  in 
the  work — a foundation  laid,  but  it  is  a safe  one.  What  has  been 


taught  will  be  a help  to  a further  pursuit  of  the  subject  should 
the  student  feel  that  he  has  developed  sufficient  talent  to  encourage 
further  study. 


Suggestion  for  treatment  of  house  showing  roof  in  light  with 
half-tone  value  to  walls. 


436 


CORINTHIAN  CAPITAL,  AND  BASE. 

Showing  conventional  shadows  and  rendering. 

Original  drawing  by  Emanuel  Brune. 

Reproduced  by  permission  of  Massachusetts  Institute  of  Technology. 


RENDERING  IN  WASH. 


All  studies  and  completed  exhibition  drawings  in  the  archi- 
tectural schools  are  tinted  in  India  ink  or  water-color.  This  is 
done  to  show  the  shadows,  and  to  indicate  the  relative  position  of 
the  different  planes,  and  is  the  method  of  representation  in  com- 
mon use  in  architects5  offices,  especially  in  the  presentation  of  com- 
petition drawings. 

MATERIALS. 

Chinese,  Japanese  or  India  inks  are  used  for  rendering,  on 
account  of  their  clear  quality  and  rich  neutral  tone.  The  ink 
comes  in  sticks,  Fig.  1,  and  it  is  ground  in  a slate  slab  provided 
with  a piece  of  glass  for  a cover.  See  Fig.  2. 


Fig.  1.  India  Ink. 


There  are  various  kinds  of  brushes.  Camel’s  hair  brushes  are 
the  cheapest  and  are  useful  for  rough  work.  Sable  brushes,  Fig. 
3,  are  two  to  three  times  as  expensive  as  the  camel’s  hair  ones  on 


Fig.  2.  Ink  Slab 

account  of  the  material,  but  are  also  very  much  better.  The  sable 
brushes  have  a spring  to  them  not  to  be  found  in  the  camel’s 
hair  brush,  and  they  come  to  a finer,  firmer  point.  Chinese  and 


441 


2 


RENDERING  IN  WASH 


Japanese  brushes  are  used  a good  deal  of  late,  as  they  are  cheaper 
than  the  sable  brushes  and  have  some  spring  to  them.  A stip- 
pling brush  is  one  with  a square  end,  used  mostly  in  china  paint- 
ing. A bristle  brush  is  a stiff  brush  used  in  oil  painting  ; on 
account  of  its  stiffness  it  is  used  for  taking  out  hard  edges,  as 
described  later  on.  Fig.  4 shows  a nest  of  porcelain  cabinet 
saucers. 


Fig.  3.  Sable  Brush. 

Besides  these  materials  the  student  should  provide  himself 
with  a large  and  a small  soft  sponge,  and  large  blotters,  which  will 
sop  up  water  readily.  Whatman’s  “ cold  pressed  ” paper  is  the 
best  paper  to  use  for  rendering  in  India  ink. 


nETHOD  OF  PROCEDURE. 

Stretching  Paper.  All  drawings  on  which  washes  are  to  be 
laid  should  be  stretched,  as  described  in  the  Mechanical  Drawing, 
Part  1. 


Fig.  4.  Nest  of  Saucers. 


Inking  the  Drawing.  The  lines  should  be  drawn  witli 
ground  India  ink,  the  ink  being  as  black  as  possible  without  being 
too  thick  to  flow.  Ornament  should  be  inked  in  with  lighter  lines 
than  the  vertical  and  horizontal  lines.  This  accents  the  struc- 
tural lines.  Very  often  the  outline  of  the  ornament  is  drawn 
in  a heavier  line  than  the  remainder.  The  width  of  the  line 


442 


RENDERING  IN  IV ASH 


n 


O 


should  vary  with  the  scale  of  the  drawing,  the  larger  and  bolder 
the  drawing  the  wider  the  line. 

India  ink  evaporates  very  rapidly.  It  should  be  kept  covered 
and  changed  several  times  a day,  especially  in  summer.  After 
the  drawing  is  inked  it  should  be  washed  to  remove  the  surplus 
ink,  otherwise  when  the  tint  is  applied  the  ink  will  spread.  This 
is  best  done  by  placing  it  under  a faucet  and  rubbino-  it  very 
dightly  with  a soft  sponge.  If  the  inking  has  been  properly  done 
the  lines  will  now  have  the  appearance  of  a firm  pencil  line  of  a 
soft  neutral  color  forming  a harmonious  background  for  the  tint. 
T1  le  shadows  should  then  be  cast  and  drawn  in  with  a hard  pencil 
in  faint  lines. 

Preparing  the  Tint.  For  large  washes  India  ink  should  be 
freshly  ground  in  a clean  saucer  each  time  it  is  required.  In  no 
case  use  the  prepared  India  ink  which  comes  in  bottles,  as  this  is 
full  of  sediment  which  settles  out  in  streaks  on  the  drawiner. 
Always  use  the  stick  ink. 

Rub  the  ink  in  the  saucer  until  it  is  very  black;  then  let  it 
stand,  keeping  the  saucer  covered.  This  allows  the  sediment, 
which  is  so  fatal  to  a clear  wash,  to  settle.  After  it  has  set- 
tled take  the  ink  from  the  top  with  a brush  without  disturbing 
the  bottom.  Put  this  ink  into  another  saucer  and  dilute  it 
with  the  necessary  amount  of  water.  Never  use  the  ink  in  the 
saucer  in  which  it  was  originally  ground.  In  dipping  the  brush 
into  the  second  saucer  it  is  well  to  take  this  ink  also  from  the 
surface  and  thus  avoid  stirring  any  sediment  wdiich  may  still 
remain  in  the  ink.  In  other  words,  the  sediment  which  is  found 
in  even  the. most  carefully  ground  ink  should  never  be  used  for 
washes,  otherwise  streaks  and  spots  may  show  in  the  washes. 

Where  only  a small  surface  is  to  be  rendered  the  tint  can  be 
mixed- on  a piece  of  paper  in  the  same  manner  in  which  it  is  mixed 
in  the  saucer.  Thus  various  shades  can  be  obtained  more  quickly 
and  experiments  made  more  easily.  Skill  in  laying  washes  is 
only  acquired  by  practice.  However,  some  instruction  is  neces- 
sary. If,  after  all  possible  care*  has  been  taken  during  the  draw- 
ing, such  as  placing  paper  under  the  hand  to  keep  the  paper  from 
getting  greasy  and  keeping  the  drawing  covered  to  protect  it  from 
the  dust,  the  paper  has  nevertheless  become  soiled,  it  should  be 


443 


4 


RENDERING  IN  WASH 


cleaned  by  giving  it  a light  sponging  with  a very  soft  sponge  and 
perfectly  clean  water.  Touch  the  surface  lightly,  sop  on  the  water 
liberally,  and  dry  it  off  immediately  with  a sponge  or  blotter  with- 
out rubbing.  Before  washing,  the  paper  should  be  cleaned  by 
rubbing  it  very  lightly  with  a soft  rubber.  Especial  care  must  be 
taken  not  to  injure  the  surface  of  the  paper  by  rubbing  too  hard. 

It  may  seem  that  all  this  care  is  unnecessary,  but  it  is  only 
by  observing  this  extreme  care  that  the  skilled  draftsman  obtains 
the  transparent  wash  and  the  beautiful,  even,  clear  tints  free  from 
all  streaks,  which  give  so  much  charm  to  an  India  ink  rendering. 

Handling  the  Brush.  Skill  in  handling  the  brush  is  acquired 
only  by  constant  practice.  The  brush  demands  great  lightness  of 
hand.  The  right  arm  should  never  support  the  body.  The  arm 
should  not  rest  on  the  drawing;  only  the  little  finger  of  the  right 
hand  should  come  in  contact  with  the  paper.  The  brush  should 
be  held  somewhat  like  a pencil  between  the  thumb  and  index 
finger,  and  the  little  finger  should  be  very  free  in  its  movements. 
Touch  the  paper  only  with  the  point  of  the  brush. 

The  brush  should  be  well  filled  with  the  tint  and  care  should 
be  taken  that  there  is  practically  the  same  amount  of  tint  in  the 
brush  at  all  times.  If  this  is  not  done,  for  example,  if  the 
brush  is  allowed  to  get  too  dry,  one  part  of  the  wash  will  dry 
faster  than  the  other  and  streaks  will  result. 

If  the  brush  should  be  too  wet,  the  surplus  moisture  can  be 
removed  by  touching  it  to  blotting  paper. 

If  the  paper  is  too  wet  the  surplus  tint  can  be  removed  by 
drying  the  brush  on  blotting  paper  and  applying  it  to  the  surplus 
tint  which  will  then  be  rapidly  absorbed  by  the  brush.  Great  care 
must  be  taken  not  to  remove  too  much  of  the  tint;  otherwise  it 
will  dry  too  fast  and  leave  a streak. 

Laying  Washes.  There  are  two  kinds  of  washes;  the  clear 
washes  used  in  rendering  shadows,  window  openings,  etc.,  and  the 
washes  in  which  the  color  is  allowed  to  settle,  the  latter  being  used 
to  render  the  grounds  surrounding  a building.  When  laying 
clear  washes  it  is  better  to  tip  the  board  slightly  so  that  the  washes 
may  flow  slowly  in  the  direction  in  which  they  are  being  carried. 
If  the  board  is  placed  flat  there  is  danger  of  the  wash  running 
back  over  the  part  that  is  already  dry  and  thus  forming  a streak. 


444 


r 


DORIC  DOORWAY  FROM  ROMAN  TEMPLE  AT  CORI,  ITALY. 

An  example  of  classic  lettering-,  conventional  shadows  and  rendering, 

Reproduced  by  permission  of  Massachusetts  Institute  of  Technology . 


RENDERING  IN  WASH 


5 


The  edge  of  the  wash  should  always  be  kept  wet,  for  if  it  begins  to 
dry  a streak  will  surely  follow.  The  tint  should  be  carried  down 
evenly  across  the  board,  moving  the  brush  rapidly  from  side  to 
side  so  that  one  side  does  not  advance  faster  than  the  other.  Carry 
the  tint  down  about  an  inch  at  a time,  the  amount  depending  upon 
the  size  of  the  brush  and  of  the  surface  rendered.  Always  go 
over  the  previous  half  inch  at  every  new  advance,  taking  care  not 
to  touch  any  part  that  has  already  dried.  In  this  way  the  tint  will 
dry  gradually,  parallel  to  the  work.  Carry  the  sides  of  the  tint 
forward  a little  more  slowly  than  the  center.  This  will  make  the 
tint  run  towards  the  center  and  help  to  avoid  the  lines  or  streaks 
due  to  uneven  drying. 

The  tint  should  be  carried  forward  in  such  a way  that  the 
paper  will  be  thoroughly  and  evenly  wet.  In  fact,  it  is  a very 
good  plan  to  dampen  the  entire  drawing  with  a soft  sponge  before 
beginning  to  lay  a wash  This  dampening  should  be  carried  well 
beyond  the  edges  of  the  drawing  so  as  to  prevent  the  color  from 
spreading  to  the  drier  and  more  absorbent  parts  of  the  paper. 
Always  remove  the  pool  of  tint  which  remains  at  the  bottom  of  a 
wash  in  the  manner  described  under  “ Handling  the  Brush.”  If 
allowed  to  remain  it  will  dry  more  slowly  than  the  rest  of  the 
drawing  and  a streak  will  show. 

The  drawing  board  should  be  left  inclined  until  the  wash  is 
dry.  Never  lay  one  wash  over  another  before  the  previous  one  is 
absolutely  dry. 

In  laying  washes  which  grade  gradually,  either  from  dark  to 
light  or  light  to  dark,  grade  the  tint  by  the  addition  of  water  or 
color  each  time  that  an  advance  is  made,  and  be  careful  that  these 
additions  are  such  that  the  change  in  color  is  made  evenly. 

It  is  very  difficult  to  lay  an  evenly  graded  dark  tint  with  one 
wash  only.  It  is  usually  better  to  lay  a light  flat  wash  or  a light 
graded  wash  to  serve  for  a background  on  which  to  lay  the  dark 
graded  wash.  By  a flat  wash  is  meant  a wash  which  is  the  same 
tone  or  color  throughout;  that  is,  a wash  that  is  not  graded.  See 
opening  in  Doric  Doorway,  Roman  Temple,  Cori,  opposite  page. 

Water  has  to  be  added  constantly  in  grading.  Where  there 
is  a series  of  graded  washes,  as  in  successive  window  openings,  it 
is  better  to  have  two  or  three  saucers  containing  tints  of  different 


447 


6 


RENDERING  IN  WASH 


strength  and  carry  each  tint  for  the  same  distance  in  each  window  so 
that  the  gradation  of  color  may  be  the  same.  In  grading  in  this  way 
it  is  necessary  to  carry  each  new  wash  well  back  over  the  old  one  so 
the  point  where  one  tint  ends  and  another  begins  may  not  show. 

Sometimes  gradations  are  obtained  by  laying  successive  flat 
washes,  each  wash  beginning  a little  lower  than  the  previous  one. 
In  this  way  the  rendered  surface  will  begin  with  one  flat  tint  and 
end  with  a number  of  tints,  one  on  top  of  the  other.  This  is  called 
the  French  method  and  is  done  by  drawing  very  faint  parallel 
lines  at  close  intervals  to  mark  the  limit  of  each  wash.  A very 
light  wash  is  then  put  over  the  whole  surface,  and  this  is  followed 
with  successive  washes,  each  starting  from  the  next  lower  line. 
This  method  is  especially  good  for  rendering  narrow,  long,  hori- 
zontal graded  washes.  See  rendering  of  mouldings  in  classical  cor- 
nice, Fig.  5.  Note  particularly  the  application  of  this  method  on 
the  crown  moulding,  and  practically  all  the  curved  mouldings. 

Avoid  laying  too  many  washes  in  the  same  place,  as  the  con- 
tinuous wetting  and  rubbing  which  the  paper  gets  from  the  brush 
is  liable  to  injure  the  surface. 

If  the  tints  are  too  dark,  a soft  sponge  can  be  used  to  lighten 
them  or  to  take  out  hard  or  dark  border  lines  ; but  a large  brush 
about  two  inches  wide  is  still  better  for  this  purpose.  If  it  is 
necessary  to  use  a sponge,  use  it  with  a great  deal  of  water,  rub 
very  lightly  and  very  patiently.  The  water  should  be  kept  very 
clean,  and  the  surrounding  parts  should  be  thoroughly  wet  before 
wetting  the  tinted  part,  otherwise  the  tint  may  spread  over  the 
other  parts  of  the  drawing.  After  using  the  sponge,  dry  the  paper 
carefully  with  a clean  blotter.  Another  and  better  way  is  to  place 
the  whole  drawincr  under  the  faucet,  turn  on  the  water  and  use  the 
sponge  or  brush,  as  already  described,  on  the  parts  to  be  lightened. 

To  make  light  places  darker,  use  the  point  of  a brush,  apply- 
ing the  tint  in  small  dots.  Be  careful  not  to  begin  with  too  dark 
a tint.  This  process  is  called  stippling,  and  it  must  be  done  very 
gradually  and  very  carefully. 

Do  not  forget  that  the  first  quality  of  a wash  is  crispness.  It 
is  necessary  to  draw  with  the  same  precision  with  a brush  as  with 
a pencil.  When  the  drawing  is  finished  it  should  be  allowed  to 
dry  thoroughly  before  it  is  cut  from  the  drawing  board. 


448 


Fig.  5.  Showing  Lights  and  Shadows  on  Classical  Cornice, 
and  French  Method  of  Rendering. 


8 


RENDERING  IN  WASH 


Rendering  Elevations.  The  object  of  rendering  a drawing 
is  to  explain  the  building.  Those  parts  of  the  building  nearest  to 
the  spectator  should  show  the  greatest  contrast  in  light  and  dark, 
for  in  nature,  as  an  object  recedes  from  the  eye,  the  contrast  be- 
comes feebler  and  feebler  and  finally  vanishes  in  a monotone. 
Every  elevation  shows  the  horizontal  and  vertical  dimensions  of  a 
building,  or  details  of  a building,  but  in  a line  drawing  the  pro- 
jections of  the  different  parts  when  in  direct  front  elevation  are  not 
shown  ; and  it  is  to  indicate  these  projections  that  the  shadows  are 
cast  and  the  drawing  is  rendered.  The  appearance  of  a building 
or  any  details  of  a building  will  be  clearly  shown  by  the  shadows 
in  their  different  values  of  light  and  dark.  (See  plates,  pages  172 
and  440.)  The  windows  and  other  openings  of  a building  should 
be  colored  dark,  but  not  black — although  this  is  sometimes  re- 
quired  in  competition  drawings — and  varying  lighter  tints  should 
be  used  to  indicate  the  color  of  the  material  in  the  roof  and  walls, 
the  difference  in  the  color  intensity  indicating  the  varying  dis- 
tances from  the  spectator.  Note  in  plate  on  page  189,  the  com- 
parative values  of  rendering  in  roof  and  shadows  on  roof  ; also 
portions  of  order  in  light,  portions  in  shadow,  and  background  of 
column.  This  method  of  drawing  is  frequently  carried  to  an  elab- 
orate extent  by  showing  high  lights,  reflected  shadows,  etc.,  and  an 
elevation  can  thus  be  made  to  show  almost  as  much  of  the  character 
of  the  proposed  building  as  would  be  shown  by  a perspective  view 
or  by  a photograph  of  the  completed  structure.  See  frontispiece, 
“ Fragments  from  Roman  Temple  at  Cori.”  Study  the  different 
tone  values  of  the  various  objects  in  the  foreground  and  in  the 
background,  and  note  the  perspective  effect  of  the  background. 

It  is  a good  plan,  before  starting  to  render  a drawing,  to  make 
a small  pencil  sketch  to  determine  the  tone  values  which  the  vari- 
ous surfaces  should  have,  so  that  they  will  assume  their  proper 
relative  positions  in  the  picture. 

Drawings  of  this  kind  are  much  superior  to  any  others  as  a 
means  of  studying  the  probable  effect  of  the  building  to  be  con- 
structed, as  they  show  the  character  of  the  building  and,  at  the 
same  time,  dimensions  can  be  figured  directly  on  the  drawing.  It 
is  difficult  and  unusual  to  give  measurements  on  a perspective 
drawing. 


450 


10 


RENDERING  IN  WASH 


Rendering  Sections  and  Plans.  Sections  are  frequently  ren- 
dered in  the  same  manner  as  elevations  to  show  the  interior  of 
buildings.  The  shadows  are  cast  in  such  a way  that  they  show  the 
dimensions  and  shapes  of  the  rooms.  The  parts  actually  in  section 
are  outlined  with  a somewhat  heavier  line  and  tinted  with  a lio-ht 

o 

tint.  The  surfaces  are  modeled  just  as  they  are  in  the  elevations. 
See  Fig.  6. 

Plans  are  rendered  to  show  the  character  of  the  different 
rooms  by  tinting  the  mosaic,  furniture,  surrounding  grounds,  trees, 
walks,  etc.  The  shadows  of  walls,  statuary,  columns  and  furniture 
are  often  cast,  so  that  the  completed  rendered  plan  is  an  architec- 
tural composition  which  tells  more  than  any  other  drawing  the 
character  of  the  finished  building. 

The  interior  of  the  building  and  all  covered  porticoes  are  left 
much  lighter  than  the  surrounding  grounds  because  the  buildincr 
is  the  most  important  portion  of  a drawing  and  should,  therefore, 
receive  the  first  attention  of  the.  spectator.  The  sharp  contrast  of 
the  black  and  white  of  the  plan  to  the  surroundings  brings  about 
the  desired  effect.  The  mosaic,  furniture,  etc.,  should  be  put  in  in 
very  light  tints  in  order  to  avoid  giving  the  plan  a spotty  look. 
The  walls  in  the  plan  should  be  tinted  dark  or  blacked  in  so  that 
they  will  stand  out  clearly.  See  Fig.  7. 

Graded  Tints.  One  rule  in  laying  all  tints  should  be  strictly 
followed  : Grade  every  wash.  A careful  study  of  the  actual 

shadows  on  buildings  will  show  that  each  shadow  varies  slightly  in 
degree  of  darkness  ; that  is,  shows  a gradation.  The  lower  parts 
of  window  openings  are,  as  a rule,  lighter  than  the  upper  parts. 
Therefore,  the  washes  or  tints  should  grade  from  dark  at  the  top 
of  the  door  or  window  openings  to  light  at  the  bottom.  Further- 
more, it  will  be  found  that  the  reflection  from  the  ground  lights  up 
shadows  cast  on  the  building,  so  that  shadows  which  are  dark  at  the 
top  become  almost  as  light  as  the  rest  of  the  building  at  its  base. 

Windows  and  doors  are  voids  in  the  facade  of  a building,  and 
they  have  a greater  value  in  the  composition  of  a design  than 
shadows  or  ornaments  in  general.  This  character  should  be  care- 
fully shown  in  the  rendering  ; and  to  that  end  the  grading  should 
never  show  such  violent  contrasts  as  to  distract  the  eye  from  the 
design  as  a whole,  and  thus  destroy  the  unity  of  the  design  and 


462 


RENDERING  IN  WASH 


11 


the  true  mass  of  the  openings.  Many  good  designs  are  greatly 
injured  in  the  rendering  by  the  violent  contrast  in  the  grading  of 
the  openings  from  dark  to  light. 

In  the  shadow  itself  it  will  be  found  that  detail  is  accented  or 


Fig.  7.  Conventional  Method  of  Rendering  Plan. 


(See  also  page  1 8.) 


458 


12 


RENDERING  IN  WASH 


brought  out  by  reflected  shadows.  These  shadows  are  in  a direc- 
tion opposite  to  the  shadows  cast  by  the  sun.  If  the  light  is 
assumed  to  come  in  the  conventional  way,  namely  at  an  angle  of 
forty -five  degrees  from  the  upper  front  left  corner  to  the  lower 
back  right  corner,  the  reflected  light  may  be  assumed  to  be  at  an 
angle  of  forty-five  degrees  from  the  lower  right  front  corner  to  the 
upper  left  rear  corner,  and  the  reflected  shadows  will  accordingly  be 
cast  in  this  direction.  See  detail  of  Greek  Doric  Order,  page  189. 

If  these  are  worked  up  in  their  correct  relation  to  one  another 
the  character  of  the  details  will  be  well  expressed. 

Distinction  Between  Different  Planes.  The  different  planes 
of  a building  which  project  one  in  front  of  the  other  are  distin- 
guished from  each  other  in  the  following  manner: 

The  parts  toward  the  front  have  a warm  color,  the  portions 
receiving  direct  light  have  a tone  over  them  indicating  the  mate- 
rial, the  shadows  are  strong  and  bold,  and  the  reflected  shadows 
are  more  or  less  pronounced.  The  parts  toward  the  rear,  on  the 
other  hand,  have  no  such  strong  contrasts  of  light  and  dark.  The 
light  parts  are  often  left  very  light  and  the  shadows  put  in  even 
tones.  The  further  the  object  is  from  the  spectator  the  less  pro- 
nounced will  be  the  reflected  lights  and  shadows.  Note  the  grad- 
ing on  the  steps  in  plate,  page  172,  and  study  the  frontispiece  as 
an  illustration  of  this  point. 

In  rendering,  a difference  should  be  made  for  different  mate- 
rials. Note  the  difference  between  the  stone  and  the  metal  work 
in  Fig.  8. 

O 

A FEW  WATER  COLOR  HINTS  FOR  DRAFTSMEN. 

Many  draftsmen  who  are  strong  in  drawing,  are  very  weak  in 
color  work.  The  reason  for  this  is,  in  most  cases,  that  the  colors 
are  not  fresh,  that  the  brush  is  too  dry,  and  that  the  color  values  are 
not  correct.  Fresh  crisp  color  is  most  important.  To  get  this 
it  is  necessary  to  start  with  a clean  color  box,  clean  brushes,  and 
clean  paints.  The  colors  should  be  moist  and  not  dry  and  hard. 

Tube  and  Pan  Colors.  After  having  acquired  some  facility 
in  the  use  of  colors,  tube  colors  are  the  best  to  use,  although 
they  are  somewhat  more  wasteful  than  pan  colors.  They  are  less 
likely  to  harden  and  dry  up  and  are  not  more  expensive.  The 


454 


Fig.  8,  Showing  Difference  in  Rendering  Stone  and  JNIetal. 


14 


RENDERING  IN  WASH 


colors  in  the  tubes  can  be  squeezed  out  on  the  palette  as  needed, 
and  if  this  is  done  fresh  bright  effects  are  obtained.  For  the  be- 


Fig.  9.  Box  for  Pan  Colors. 


ginner,  however,  pan  colors  are  recommeded,  as  they  are  more 
easy  to  handle.  Fig.  9 shows  a japanned  tin  box  for  pan  colors. 
Fig.  10  shows  a pan  color,  and  Fig.  11  a tube  color. 

List  of  Colors:  The  following;  list  of  colors  will  make  a 

very  good  palette: 


Cadmium 
Indian  Yelloiv 
Lemon  Yellow 
Gallstone 
Yellow  Ochre 


Orange  Vermilion 
Carmine 
Light  Red 
Burnt  Sienna 
Warm  Sepia 


Cobalt  Blue 
New  Blue 
Prussian  Blue 
I aine's  Gray 


Emerald  Green 
Hooker's  Green 

Chinese  White 


The  colors  printed  in  italics  are  clear  colors  which  will  give 
clear  even  washes.  The  others  will  settle  out,  the  color  settling 


Fig.  10.  Pan  Color. 


WINS  OR  & NEWTON 

i^iW  If 

TJatHbene  Place.  LTD,, 

tj]  1) j 

LONDON.  ENGLAND 

I;  ' -1  - 

MOIST  COLOUR. 

li 

■HE 

^COBALT  BLUF.  S 

01 

Fig.  11.  Tube  Color. 


into  the  pores  of  the  paper  producing  many  small  spots.  This 
effect  is  often  desirable,  giving  a texture  which  cannot  be  obtained 
with  the  clear  colors. 


456 


RENDERING  IN  WASH 


15 


For  use  in  the  offices,  India  ink,  Chinese  white,  gallstone, 
carmine  and  indigo  will  be  found  very  convenient.  The  latter 
three  are  convenient  forms  of  the  three  primary  colors  to  use  with 
India  ink  in  rendering.  Many  draftsmen  use  these  alone. 

manipulation.  The  washed-out  look  of  many  of  the  color 
sketches  seen  in  architectural  exhibitions  is  very  noticeable.  The 
sketches  lack  strength  and  crispness. 

Color  properly  applied  should  be  put  on  boldly  in  broad 
simple  washes  without  fear  of  too  much  color.  Remember  that 
colors  when  dry  are  much  lighter  than  when  in  a moist  state.  Use 
plenty  of  clear  water  in  the  brush.  Do  not  go  over  one  wash  with 
another  before  the  first  is  entirely  dry.  This  is  particularly  true 
where  a deeper  tone  is  to  be  put  over  a lighter  one.  In  broad  sky 
washes  where  there  is  a great  deal  of  paper  to  be  covered,  dampen 
the  surface  well  first  with  a small  sponge,  then  with  a large  brush 
and  bold  yet  light  quick  strokes  put  in  the  sky. 

Brushes  and  Paper.  A small  brush  with  a good  point  is 
necessary  for  “ drawing  in  ” and  for  detail.  A bristle  brush  is  very 
useful  to  remove  color  and  to  soften  hard  lines.  Chinese  brushes 
are  very  good,  as  they  hold  a great  deal  of  color  and  at  the  same 
time  have  a good  point. 

If  an  edge  shows  a hard  line,  this  can  be  softened  by  dipping 
the  bristle  brush  into  clean  water  and  rubbing  the  point  lightly 
over  the  edge  that  is  too  hard,  sopping  up  the  water  at  frequent 
intervals  with  a clean  blotter.  It  is  important  that  plenty  of  clean 
water  should  be  used  and  that  the  water  be  taken  up  with  a blotter 
very  often 

AYhen  a “high  light”  is  lost,  and  a bristle  brush  does  not 
take  out  enough  color,  the  “high  light”  may  be  put  in  with 
Chinese  white,  mixing  it  with  a little  of  the  color  of  the  material. 

Look  at  your  subject  broadly  and  do  not  try  to  put  in  too 
many  details.  Whatman’s  hot  pressed  70-  or  90-lb.  paper  is  good 
to  use.  The  hot  pressed  paper,  which  has  a smooth  surface,  takes 
the  color  better  than  the  rough  surfaced  or  cold  pressed  paper,  but 
the  cold  pressed  has  more  texture  and  gives  better  atmospheric 
effects. 

Combination  of  Color.  For  the  inexperienced  a few  hints  as 
to  what  combinations  of  color  to  use  may  be  helpful.  It  must 


457 


16 


RENDERING  IN  WASH 


always  be  remembered  that  the  colors  must  be  clean  to  get  fresh 
bright  effects. 

O 

A simple  blue  sky:  Prussian  Blue,  Antwerp  Blue  or  Cobalt  Blue. 
Clouds:  Light  Bed.  For  the  distance  use  lighter  tones  with  the 
addition  of  a little  Emerald  Green  or  Carmine. 

Dark  part  of  clouds:  Light  Bed  and  New  Blue. 

Boads  and  pathways  in  sunlight  : Yellow  Ochre  and  Light  Bed  with 
a little  New  Blue  to  gray  it. 

Cast  shadows:  Cobalt  and  Light  Bed  or  Carmine  with  a little  green 
added. 

Grass  in  sunlight:  Lemon  Yellow  and  Emerald  or  Hooker’s  Green; 

or  Indian  Yellow  and  Emerald  Green. 

Grass  in  shadow:  Prussian  Blue  and  Indian  Bed;  or  Prussian 
Blue  and  Burnt  Sienna.  Aurora  Yellow  and  Prussian  Blue 
gives  a green  color  similar  to  Emerald. 

For  gray  roofs  in  sunlight:  Light  Bed  and  New  Blue. 

Primary,  Secondary  and  Complementary  Colors.  The  com- 
bination of  colors  maybe  learned  by  means  of  the  diagram,  Fig.  12, 
which  will  assist  the  student  greatly  in  his  water  color  work.  The 
three  primary  colors  are  yellow,  red  and  blue.  The  combination 

of  any  two  of  these  will  give  a sec- 
ondary color — orange,  purple  or 
green.  Two  colors  are  called  com- 

o 

plementary  colors  if  the  one  is  com- 
posed of  two  of  the  primary  colors 
and  the  other  one  is  the  third  pri- 
mary color.  Thus,  green,  composed 
of  the  primary  colors  blue  and  yel- 
low, has  as  complementary  color  the 
third  primary  color;  i.e.,  red.  Con- 
sulting the  diagram  it  will  be  found 
that  opposite  colors  are  complemen- 
tary colors;  i.e  , blue  and  orange, 
red  and  green,  yellow  and  purple.  If  two  complementary  colors  are 
put  alongside  of  one  another,  each  color  will  look  brighter  along- 
side the  other  than  if  plaeed  by  itself;  this  is  due  to  the  law  of 
contrasts.  Thus,  the  same  green  if  placed  alongside  red,  will  look 
greener  than  when  by  itself,  and  the  same  holds  good  for  the 


458 


RENDERING  IN  WASH 


17 


red.  If  complementary  colors  are  mixed  together  you  get  a softer 
color,  a gray  and  sometimes  muddy  effect.  If  blue,  red  and  yel- 
low are  mixed  together  in  the  right  proportion  a soft  gray  is 
obtained 

Water  Color  Rendering.  Where  colors  are  used  for  architec- 
tural drawings  they  should  be  mixed  fresh,  if  clear  tints  are  wanted, 
but  in  places  where  it  is  desired  to  have  certain  effects  obtained  by 
allowing  color  to  settle,  tints  that  have  stood  some  time  may  be 
used.  Especially  is  this  true  for  plans,  where  the  color  is  allowed 
to  settle  in  putting  in  grass,  trees,  statues,  etc.  When  it  is  desired 
to  let  the  color  settle  it  is  better  to  leave  the  board  flat  and  carry 
the  color  along  with  the  brush,  leaving  it  until  it  is  dry.  Some 
draftsmen  keep  the  board  level  for  all  their  work. 

Sketch  elevations  in  pencil  may  be  inked  in  or  may  be  ren- 
dered directly  in  water  color,  the  shadows  being  cast  and  various 
colored  tints  laid  on  to  show  the  different  materials,  shadows,  win- 
dow openings,  etc. 

Sketches  rendered  in  sepia  only  are  very  effective,  putting  in 
the  lines  with  the  pen,  and  rendering  with  light  sepia  washes. 
Elevations  are  usually  most  effective  when  the  shadows  are  put  in 
by  washes  that  grade  quickly  from  dark  to  light,  brilliancy  is  thus 
obtained.  It  is  astonishing  what  effects  can  be  obtained  with  very 
faint  washes.  This  applies  especially  to  small  scale  drawings. 
The  larger  the  scale  of  the  building  or  detail,  the  stronger  should 

be  the  coloring  and  values  of  light  and  dark. 

© © 

When  sections  are  colored  the  parts  actually  in  section  are 
outlined  with  a strong  red  line  and  tinted  a very  light  pink.  The 
colors  on  the  wall  are  merely  suggested. 

On  the  plans  the  mosaic,  furniture,  etc.,  is  often  shown  in  a 
light  pink.  Where  a statue  has  a prominent  place  it  is  put  in  in 
strong  vermilion.  Attention  is  called  here  to  the  fact  that  letter- 
ing on  a plan  counts  as  mosaic,  and  should  be  done  in  such  a way 
that  it  will  help  the  effect  sought  for,  a very  important  point  to 
remember  in  competition  drawings. 

The  important  thing  to  remember  in  rendering  is  to  get  the 
correct  relative  value  of  lights  and  darks.  To  do  this  it  is  neces- 
sary to  have  clearly  in  mind  what  the  important  features  to  be 
brought  out  are  and  what  is  the  most  direct  way  of  accomplishing 


459 


18 


RENDERING  IN  WASH 


this  ; in  other  words,  the  aim  should  be  to  make  as  harmonious  a 
composition  as  taste,  talent  and  thought  can  produce. 

Water  Color  Sketching.  Nothing  is  more  useful  to  an  archi- 
tectural draftsman  than  out-of-door  sketching  in  colors.  A water 
color  block  should  be  his  constant  companion  on  his  Saturday  half 
holidays,  and  if  possible,  he  should  join  some  sketching  class. 

The  sketches  in  water  color  may  be  taken  from  natural  scenery, 
but  the  student  should  also  make  studies  and  color  sketches  from 
color  decorations  of  exterior  and  interior  of  buildings. 

Do  not  indicate  too  much  in  water  color  sketching,  search  for 
the  big  masses  in  shape  and  color  values  and  put  them  in  direct 
and  simple. 

A draftsman  who  gives  his  leisure  time  to  water  color  sketch- 
ing in  summer,  and  to  evening  classes  in  drawing  from  the  antique 
and  from  life  in  winter,  will  have  as  good  a training  as  could  be 
wished  for  in  this  part  of  his  architectural  career. 


460 


EXAMINATION  PAPER 


PLATE  A 


RENDERING  IN  WASH. 


General  Remarks.  Whatman’s  cold  pressed  paper  is  the 
best  for  these  examination  plates.  The  Imperial  size  is  22  in.  X 
30  in.,  and  one  of  these  sheets  will  cut  into  two  sheets  15  in.  X 22 
in.,  which  will  be  large  enough  for  all  of  the  examination  plates. 
The  lines  are  to  be  inked  with  India  ink,  after  which  the  drawing 
is  to  be  washed  before  rendering.  The  lines  must  be  drawn  very 
neatly  and  carefully. 

Before  starting  to  render,  small  pencil  sketches  should  be 
made  to  study  the  relations  of  the  lights  and  shadows  and  to  deter- 
mine their  values.  The  student  will  find  that  with  the  aid  of  such 
pencil  sketches,  he  can  render  with  greater  accuracy,  and  will 
obtain  quicker  and  better  results. 

The  shadows  in  plates  C to  E are  indicated  by  dotted  lines. 
In  the  finished  drawings,  these  should  be  shown  in  fine  light  full 
pencil  lines. 

In  fastening  the  paper  to  the  board,  care  must  be  taken  not 
to  allow  the  paste  to  extend  more  than  half  an  inch  back  from  the 
edge  of  the  paper. 

Be  sure  to  write  your  name  and  address  legibly  on  the  back 
of  each  drawing. 

PLATE  I. 

This  plate  is  to  be  three  times  the  size  of  plate  A and  the 
different  rectangles  are  to  be  rendered  as  follows: 

Rectangle  A,  with  a light  even  wash  similar  in  tone  to  “ High 
Light”  in  the  value  scale: 

Rectangle  B,  with  a medium  even  wash  similar  to  “ Middle”: 
Rectangle  C,  with  a very  dark  even  wash  similar  in  tone  to  ‘‘Dark”: 
Rectangle  D has  various  compartments  which  are  to  be  rendered 
with  an  even  wash  having  the  same  tone  in  each  compartment 
similar  to  “ Low  Light”: 

Rectangle  E,  with  a medium  even  wash  similar  to  **  Middle”,  leav- 
ing the  four  enclosed  spaces  “ White”: 


493 


m 


- 


jO 

L v 'd 
■ 


liffl 

L > 


/TV/?] 

Or 


/~&\ 


PLATE  B 


RENDERING  IN  WASH 


Rectangle  F,  with  alternating  dark  and 
medium  stripes,  the  first,  third,  fifth 
and  seventh  stripe  to  be  dark,  similar 
to  “ High  Dark”,  the  others  light  sim- 
ilar to  u Low  Light”: 

Rectangle  G has  various  strips  which  are 
to  he  graded  evenly,  the  top  strip  be- 
ing the  darkest,  the  next  one  a little 
lighter  and  so  on  until  the  last  strip 
is  very  light  in  tone.  The  successive 
values  of  the  strips  should  be  “ Dark”, 
“High  Dark”,  “Middle”,  “Low 
Light”,  “Light”  and  “High  Light”: 

Rectangle  H,  with  a graded  wash  varying 
from  dark  at  the  top  to  light  at  the 
bottom.  Care  should  be  taken  to  have 
the  wash  evenly  graded.  The  dark 
should  be  similar  in  value  to  “ High 
Dark”  and  the  light  similar  to  “ Low 
Light”: 

Rectangle  I,  with  a graded  wash  varying 
from  light  at  the  top  to  dark  at  the 
bottom.  In  rendering  this  rectangle 
the  board  should  not  be  turned  around 
and  the  wash  put  on  by  grading  from 
light  to  dark,  but  the  board  should  be 
left  in  the  same  position  and  the  wash 
graded  by  the  admixture  of  color  in- 
stead of  water.  The  light  should  be 
similar  to  “ Light”  and  the  dark  sim- 
ilar to  “Middle”: 

Rectangle  J,  with  a graded  wash  varying 
from  dark  to  light,  the  spaces  between 
the  two  halves  of  the  rectangle  being 
left  “ White”.  The  dark  is  similar 
to  “ Middle”  and  the  light  similar  to 
“ Light”. 


■■■•/J 


Light 


VALUE  SCALE. 


465 


PLATE  C 


RENDERING  IN  WASH 


25 


The  Value  Scale  is  given  merely  to  show  the  relative  degrees  of  dark- 
ness, not  to  show  the  actual  appearance  of  the  wash.  The  wash  itself  must 
be  perfectly  clear  and  transparent 

Note.  The  various  values  should  not  be  made  in  one  wash.  Better 
effects  are  obtained  by  superimposing  several  light  washes  and  thus  obtain- 
ing a dark  wash,  than  by  putting  on  a dark  wash  in  one  operation. 

PLATE  II. 

This  plate  is  to  be  drawn  three  times  the  size  of  plate  B.  The 
section  of  the  mouldings  is  to  be  drawn  first,  then  lines  drawn  at 
an  angle  of  45°  from  the  different  corners  of  the  mouldings.  The 
vertical  surfaces  are  to  be  rendered  darker  than  the  horizontal  ones 
as  shown  in  the  top  moulding  in  the  first  column.  The  mould- 
ings in  the  second  and  fourth  columns  are  to  be  rendered  by  the 
French  method,  drawing^*?  light  parallel  pencil  lines  and  render- 
ing by  successive  washes,  as  shown  in  the  rendered  illustrations. 
The  mouldings  in  the  third  and  fifth  columns  are  to  be  rendered 
by  grading  directly,  by  the  addition  of  water  if  the  tone  changes 
from  dark  to  light  or  by  the  addition  of  tint  if  the  tone  chancres 
from  light  to  dark.  The  letters  and  the  border  lines  are  to  be 
rendered  as  indicated.  A margin  of  half  an  inch  of  white  paper 
is  to  be  left  outside  of  the  border  lines. 

PLATE  III. 

Rendering  of  Doric  Order.  This  plate  is  to  be  three  times 
the  size  of  plate  C.  The  order  is  the  same  size  as  the  order  on  plate 
VII,  in  the  Roman  Orders.  For  rendering  the  order,  the  plate 
on  page  189,  “ Detail  of  Greek  Doric  Order”,  will  serve  as  a guide. 
The  background  A should  be  graded  from  dark  at  the  top  to  light 
at  the  bottom  similar  to  the  wash  between  the  column  and  pilaster 
in  the  plate  mentioned  above.  The  mouldings  may  be  put  in  by 
the  French  method  as  shown  in  Fig.  5.  The  background  B should 
be  a light  evenly  graded  wash  similar  to  the  upper  part  of  the 
background  in  the  frontispiece,  “ Fragments  from  Roman  Temple”, 
having  the  wash  somewhat  darker  at  the  top  and  grading  it  out  to 
very  light  at  the  bottom.  No  trees,  etc.,  are  to  be  shown  in  the 
background.  The  steps  will  have  a very  light  wash,  that  on  step 
C being  hardly  noticeable,  the  step  D a slightly  more  pronounced 
wash,  and  the  step  E a little  darker  still,  but  very  light  in  tone. 
Study  the  value  scale  to  determine  these  gradations.  The  tablet 
with  letters  may  be  rendered  similar  to  the  tablet  at  the  bottom  of 


467 


RENDERING  IN  WASH 


26 


the  plate  mentioned  above.  Reflected  shadows  are  to  be  put  in 
and  care  should  be  taken  to  show  the  reflected  lights  in  the  shade. 

o 

PLATE  IV 

T1  lis  plate  is  to  be  drawn  double  the  size  of  plate  D.  A mar- 
gin one  and  one-half  inches  is  to  be  left  as  a white  border  outside 
the  border  line.  The  “ Doric  Doorway  from  Roman  Temple  at 
Cori”,  page  446,  will  serve  as  a guide  for  rendering  this  plate. 
The  window  opening  is  to  be  rendered  with  an  even  dark  wash, 
and  the  wall  surface  is  to  have  a light  tone.  The  shadows  are 
indicated  by  a faint  wash  and  are  to  be  modeled  and  graded  m 
such  a way  that  they  all  have  proper  relative  values.  \ 

PLATE  V. 

This  plate  is  to  be  drawn  double  the  size  of  plate  E,  and  a 
margin  of  an  inch  and  a half  of  white  is  to  be  left  outside  of  the 
border  line.  Plate  XXXI II,  in  the  Roman  Orders,  can  be  used  as  a 
guide,  the  Temple  drawn  there  being  of  the  same  size  required  for 
this  problem.  If  the  flutes  on  the  columns  are  put  in,  they  should 
be  drawn  with  watered  ink  so  that  they  are  not  too  pronounced. 
The  shadows  and  the  parts  in  shade  are  shown  by  a faint  flat  wash 
outlined  by  dotted  lines.  All  the  lights  and  shadows  are  to  be 
carefully  modeled  in  their  proper  relations  to  one  another.  The 
wall  Aj  and  A2  is  on  a line  with  the  rear  wall  of  the  Temple; 
hence  the  portion  of  the  wall,  A2,  on  the  right  of  the  Temple  will 
be  in  shade,  and  the  portion,  A . on  the  left  will  have  a light  tone 
over  it  to  show  that  it  is  in  the  background.  For  the  rendering 
of  the  spaces  between  the  columns  ana  the  doorway,  the  plate 
14  Detail  from  Temple  of  Mars  Vengeur”,  page  172,  will  be  help- 
ful as  well  as  for  the  rendering  of  the  steps.  The  shadows  on  the 
steps  will  be  similar  in  grading  to  the  shadow  of  the  altar  on  the 
steps.  The  bronze  candelabra  is  to  be  rendered  dark,  care  being 
taken  to  leave  high  lights  of  u White”  on  the  round  surfaces 
receiving  the  most  direct  light.  For  suggestions  for  rendering 
the  bronze  see  Fig.  8.  In  rendering  background,  the  frontispiece, 
44  Fragments  from  Roman  Temple  at  Cori”,  will  prove  helpful. 


468 


PLATE  D 


PLATE  E 


Fig.  21.  Study  for  Lettering  on  Granite  Frieze  of  Boston  Public  Library, 
McKim,  Mead  & White,  Architects. 


ARCHITECTURAL  LETTERING 


Architectural  lettering  may  be  divided  into  two  general 
classes.  The  first  is  for  titling  and  naming  drawings,  as  well  as 
for  such  notes  and  explanations  as  it  is  usual  or  necessary  to  put 
upon  them;  this  may  well  be  called  “Office  Lettering.”  The 
second  includes  the  use  of  letters  for  architectural  inscriptions 
to  be  carved  in  wood  or  stone,  or  cast  in  metal:  for  this  quite  a 
different  character  of  letter  is  required,  and  one  that  is  always 
to  be  considered  in  its  relation  to  the  material  in  which  it  is  to 
be  executed,  and  designed  in  regard  to  its  adaptability  to  its 
method  of  execution.  This  may  be  arbitrarily  termed  “Inscrip- 
tion Lettering,”  and  as  a more  subtle  and  less  exact  subject  than 
office  lettering  it  may  better  be  taken  up  last. 

OFFICE  LETTERING. 

Architectural  office  lettering  has  nothing  in  common  with 
the  usual  Engineering  letter,  or  rather,  to  be  more  exact,  the  re- 
verse is  true : Engineering  lettering  has  nothing  in  common  with 
anything  else.  Its  terminology  is  wrong  and  needlessly  confusing 
inasmuch  as  it  clashes  with  well  and  widely  accepted  definitions. 
Therefore  it  will  be  necessary  to  start  entirely  anew,  and  if  the 
student  has  already  studied  any  engineering  book  on  the  subject, 
to  warn  him  that  in  this  instruction  paper  such  terms  as  Gothic, 
etc.,  will  be  used  in  their  well-understood  Architectural  meaning 
and  must  not  be  misinterpreted  to  include  the  style  of  letter 
arbitrarily  so  called  by  Engineers. 

The  first  purpose  of  the  lettering  on  an  architectural  plan  or 
elevation  is  to  identify  the  sheet  with  its  name  and  general 
descriptive  title,  and  further,  to  give  the  names  of  the  owner 
and  architect.  The  lettering  for  this  purpose  should  always  be 
rather  important  and  large  in  size,  and  its  location,  weight  and 


473 


4 


ARCHITECTURAL  LETTERING 


height  must  be  exactly  determined  by  the  size,  shape  and  weight 
of  the  plan  or  elevation  itself,  as  well  as  its  location  upon  and 
relation  to  the  paper  on  which  it  is  drawn,  in  order  to  give  a 
pleasing  effect  and  to  best  finish  or  set  off  the  drawing  itself. 
The  style  of  letter  used  may  be  suggested,  or  even  demanded,  by 
the  design  of  the  building  represented.  Thus  Gothic  lettering 
might  be  appropriate  on  a drawing  of  a Gothic  church,  just  as 
Italian  Renaissance  lettering  would  be  for  a building  of  that 
style,  or  as  Classic  lettering  would  seem  most  suitable  on  the 
drawings  for  a purely  Classic  design;  while  each  letter  or  legend 
would  look  equally  out  of  place  on  any  one  of  the  other  drawings. 

LETTER  FORHS. 

It  may  be  said  that  practically  all  the  lettering  now  used 
in  architectural  • offices  in  this  country  is  derived,  however  re- 
motely it  may  seem  in  some  cases,  from  the  old  Roman  capitals 
as  developed  and  defined  during  the  period  of  the  Italian  Renais- 
sance. These  Renaissance  forms  may  be  best  studied  first  at  a 
large  size  in  order  to  appreciate  properly  the  beauty  and  the 
subtlety  of  their  individual  proportions.  For  this  purpose  it  is 
Avell  to  draw  out  at  rather  a large  scale,  about  four  or  four  and 
one-half  inches  in  height,  a set  of  these  letters  of  some  recognized 
standard  form,  and  in  order  to  insure  an  approximately  correct 
result  some  such  method  of  construction  as  that  shown  in  Figs. 
1 and  2 should  be  followed.  This  alphabet,  a product  of  the 
Renaissance,  though  of  German  origin,  is  one  adapted  from  the 
well-known  letters  devised  by  Albrecht  Diirer  about  1525,  and  is 
here  merely  redrawn  to  a simpler  constructive  method  and  ar- 
ranged in  a more  condensed  fashion.  This  may  be  accepted  as  a 
good  general  form  of  Roman  capital  letter  in  outline,  although 
it  lacks  a little  of  the  Italian  delicacy  of  feeling  and  thus  be- 
trays its  German  origin. 

The  letter  is  here  shown  in  a complete  alphabet,  including 
those  letters  usually  omitted  from  the  Classic  or  Italian  inscrip- 
tions: the  J,  U (the  V in  its  modern  form)  and  two  alternative 
W’s,  which  are  separately  drawn  out  in  Fig.  1. 

These  three  do  not  properly  form  part  of  the  Classic  alpha- 
bet and  have  come  into  use  only  within  comparatively  modern 


474 


ARCHITECTURAL  LETTERING 


5 


times.  For  this  reason  in  any  strictly  Classic  inscription  the 
letter  I should  be  used  in  place  of  the  J,  and  the  V in  place 
of  the  U.  It  is  sometimes  necessary  to  use  the  W in  our  modern 
spelling,  when  the  one  composed  of  the  double  V should  always 
be  employed. 

The  system  of  construction  shown  in  this  alphabet  is  not 
exactly  the  one  that  Diirer  himself  devised.  The  main  forms 
of  the  letters  as  well  as  their  proportions  are  very  closeiy  copied 
from  the  original  alphabet,  but  the  construction  has  been  some- 
what simplified  and  some  few  minor  changes  made  in  the  letters 
themselves,  tending  more  towards  a modern  and  more  uniform 
character.  The  two  W’s,  one  showing  the  construction  with  the 
use  of  the  two  overlapping  letter  V’s,  and  one  showing  the  W 
incorporated  upon  the  same  square  unit  which  carries  the  other 


Fig.  1.  Two  Alternative  Forms  of  the  Letter  W, 
to  accompany  the  Alphabet  shown  in  Fig.  2. 


letters  (the  latter  form  being  the  one  used  by  Diirer  himself), 
are  shown  separately  in  Fig.  1.  It  should  be  noticed  that  every 
letter  in  the  alphabet,  except  one  or  two  that  of  necessity  lack 
the  requisite  width — such  as  the  I and  J — is  based  upon  and 
fills  up  the  outline  of  a square,  or  in  the  case  of  the  round  letters, 
a circle  which  is  itself  contained  within  the  square.  This  alpha- 
bet should  be  compared  with  the  alphabet  in  Fig.  4,  attributed 
to  Sebastian  Serlio,  an  Italian  architect  of  the  sixteenth  century. 
By  means  of  this  comparison  a very  good  idea  may  be  obtained 
of  the  differences  and  characteristics  which  distinguish  the  Italian 
and  German  traits  in  practically  contemporaneous  lettering. 

After  once  drawing  out  these  letters  at  a large  size,  the  be- 
ginner may  find  that  he  has  unconsciously  acquired  a better  con- 
structive feeling  for  the  general  proportions  of  the  individual  let- 


475 


6 


ARCHITECTURAL  LETTERING 


ters  and  should  thereafter  form  the  letters  free-hand  without  the 
aid  of  any  such  scheme  of  construction,  merely  referring  occa- 
sionally to  the  large  chart  as  a sort  of  guide  or  check  upon  the 


Fig.  2.  Alphabet  of  Classic  Renaissance  Letters  according  to  Albrecht 
Diirer,  adapted  and  reconstructed  by  F.  C.  Brown.  (See  Fig.  1.) 


eye.  For  this  purpose  it  should  be  placed  conveniently,  so  that  it 
may  be  referred  to  when  in  doubt  as  to  the  outline  of  any  in- 
dividual letter.  By  following  this  course  and  practicing  thor- 


476 


ARCHITECTURAL  LETTERING 


( 


oughlv  the  use  of  the  letters  in  word  combinations,  a ready  com- 
mand over  this  important  style  of  letter  will  eventually  be 
acquired. 


Fig.  2.  (Continued) 


In  practice  it  will  soon  be  discovered  that  a letter  in  outline 
and  of  a small  size  is  more  difficult  to  draw  than  one  solidly 
blacked-in,  because  the  defining  outline  must  be  even  upon  both 


477 


8 


ARCHITECTURAL  LETTERING 


its  edges ; and  that  as  the  eye  follows  more  the  inner  side  of  this 
line  than  it  does  the  outer,  both  in  drawing  and  afterwards  in 
recognizing  the  letter  form,  the  inaccuracies  of  the  outer  side  of 
the  line  are  likely  to  show  up  against  the  neighboring  letters,  and 
produce  an  irregularity  of  effect  that  it  is  difficult  to  overcome, 
especially  for  the  beginner;  while  in  a solidly  blacked-in  letter, 
it  is' the  outline  and  proportions  alone  with  which  the  draftsman 
must  concern  himself.  Therefore,  a letter  in  the  same  style  is 
more  easily  and  rapidly  drawn  when  solidly  blacked-in  than  as 
an  “open”  or  outline  letter.  In  many  cases  where  it  is  desired 
to  give  a more  or  less  formal  and  still  sketchy  effect,  a letter  of 
the  same  construction  but  with  certain  differences  in  its  charac- 
teristics may  be  used.  It  should  not  be  so  difficult  to  draw,  and 
much  of  the  same  character  may  still  be  retained  in  a form  that 


TAVNTON'PVBLIC'  LIBRA  R V 
TAVNTON  ' M A A A A C H V >5  E T T 5 

ALBERT  RANDOLPH  RO.S.5  ARCHITECT  ONE  HUNDRED  AND  FIFTY  SIX  FIFTH  AVENUE  NEW  YORK  CITY 


Fig.  3.  Title  from  Competitive  Drawings  for  the  Taunton  Public  Library, 
Albert  Randolph  Ross,  Architect. 


is  much  easier  to  execute.  Some  such  letter  as  is  shown  at  the 
top  of  Fig.  10,  or  any  other  personal  variation  of  a similar  form 
such  as  may  be  better  adapted  to  the  pen  of  the  individual  drafts- 
man would  answer  this  purpose.  The  titles  shown  in  Figs.  3 and 
5 include  letters  of  this  same  general  type,  but  of  essentially 
different  character. 

In  drawing  a letter  that  is  to  he  incised  in  stone  it  is  cus- 
tomary to  show  in  addition  to  the  outline,  a third  line  about  in 
the  center  of  the  space  between  the  outside  lines.  This  addi- 
tional line  represents  the  internal  angle  that  occurs  at  the  meeting 
of  the  two  sloping  faces  used  to  define  the  letter.  An  example  is 
shown  in  Figs.  24  and  25,  while  in  Fig.  7,  taken  from  drawings 
for  a building  by  McKim,  Mead  & White,  the  -same  convention 
is  frankly  employed  to  emphasize  the  principal  lettering  of  a 
pen-drawn  title. 


478 


ARCHITECTURAL  LETTERING 


9 


Fig.  4.  Italian  Renaissance  Alphabet,  according  to  Sebastian  Serlio. 


479 


10 


ARCHITECTURAL  LETTERING 


For  the  purpose  of  devising  a letter  that  may  be  drawn  with 
one  stroke  of  the  pen  and  at  the  same  time  retain  the  general 
character  of  the  larger,  more  Classic  alphabet,  in  order  that  it 
may  be  consistently  used  for  less  important  lettering  on  the  same 
drawing,  it  is  interesting  to  try  the  experiment  of  making  a 
skeleton  of  the  letters  in  Figs.  1 and  2.  This  consists  in  running 
a single  heavy  line  around  in  the  middle  of  the  strokes  that  form 


JERSEY-  GTY  • FREE  ’ PVBLIC  * LIBRARY 

-SCALE  - QNE’JNCH  - Ej3V\LS  - KM  - FEET  • 

BRJTL  * AND  - BACON  * ARCHITECTS  * IlIFlFlE  ^AVENVE*  NEW  ^ YORK*  QIY- 

Fig.  5.  Title  from  Drawings  for  the  Jersey  City  Public  Library, 
Brite  & Bacon,  Architects. 


the  outline  of  these  letters.  This  “skeleton”  letter,  with  a few 
modifications,  will  be  found  to  make  the  best  possible  capital 
letter  for  rapid  use  on  working  drawings,  etc.,  and  in  a larger 
size  it  may  be  used  to  advantage  for  titling  details  (Fig.  9).  It 
will  also  prove  to  be  singularly  effective  for  principal  lettering 


on  plans,  to  give  names  of  rooms,  etc.  (Fig.  13),  while  in  a still 
smaller  size  it  may  sometimes  be  used  for  notes,  although  a 
minuscule  or  lower  case  letter  will  be  found  more  generally  useful 
for  this  purpose. 

In  Fig.  6 are  shown  four  letters  where  the  skeleton  has  been 
drawn  within  the  outline  of  the  more  Classic  form.  It  is  un- 


480 


ARCHITECTURAL  LETTERING 


11 


o 

e 


< 


tU 

o 

& 

Ols 

2 


necessary  to  continue  this  experi- 
ment at  a greater  length,  as  it  is 
believed  the  idea  is  sufficiently  de- 
veloped in  these  four  letters.  In 
addition  it  is  merely  the  theoreti- 
cal part  of  the  experiment  that  it 
is  desirable  to  impress  upon  the 
draftsman.  In  practice  it  will  be 
found  advisable  to  make  certain 
further  variations  from  this  “skel- 
eton” in  order  to  obtain  the  most 
pleasing  effect  possible  with  a 
single-line  letter.  But  the  basic 
relationship  of  these  two  forms 
will  amply  indicate  the  propriety 
of  using  them  in  combination  or 
upon  the  same  drawing. 

It  will  be  found  that  the  letter 
more  fully  shown  in  Fig.  10  is 
almost  the  same  as  the  letter  pro- 
duced by  this  “skeleton”  method, 
except  that  it  is  more  condensed. 
That  is,  the  letters  are  narrower 
for  their  height  and  a little  freer 
or  easier  in  treatment.  This 
means  that  they  can  be  lettered 
more  rapidly  and  occupy  less 
space,  and  also  that  they  will  pro- 
duce a more  felicitous  effect. 

In  actual  practice,  the  free  cap- 
itals shown  in  Fig.  10  will  be 
found  to  be  of  the  shape  that  can 
be  made  most  rapidly  and  easily, 
and  this  style  or  some  similar  let- 
ter should  be  studied  and  practiced 
very  carefully. 

Other  examples  of  similar 
one-line  capitals  will  be  found 


481 


12 


ARCHITECTURAL  LETTERING 


used  with  classic  outline  or  blacked-in  capitals  on  drawings, 
Figs.  3,  5 and  7. 

In  Figs.  8,  9 and  13  these  one-line  letters  are  used  for 
principal  titles  as  well,  and  with  good  effect. 

In  Fig.  10  is  shown  a complete  alphabet  of  this  single-line 

blLl  OF  INDIANA  LIMESTONE 
QENESEE  VALLEY  TRJ/ST  COS  bVILDINAi 

Fig.  8.  Title  from  Architectural  Drawing,  Claude  Fayette  Bragdon,  Architect. 

letter,  and  the  adaptability  of  this  character  for  use  on  details  is 
indicated  by  the  title  taken  from  one  and  reproduced  in  Fig.  9. 
In  the  same  plate,  Fig.  10,  is  also  shown  an  excellent  form  of 
small  letter  that  may  he  used  with  any  of  these  capitals.  It  is 


o. 


22)  OF 


Frejtonf  Jhelt  C 


405  ■ COAmONWEALTtt  Avl 

v_/e pCember  - <2>  ® ^ * 

Frank  - Chouteau  - brown  -Architect- 

N ° \3  * PoLrko  -cjtreet-  Maair  • 


Fig.  9.  Title  from  Detail. 

quite  as  plain  as  any  Engineer’s  letter,  and  is  easier  to  make, 
and  at  the  same  time  when  correctly  placed  upon  the  drawing 
it  is  much  more  decorative.  This  entire  plate  is  reproduced  at 
a slight  reduction  from  the  size  at  which  it  was  drawn,  so  that 
it  may  he  studied  and  followed  closely. 


482 


ARCHITECTURAL  LETTERING 


13 


- LETTERS  FOR- 
- PRINCIPAL- 
TITLES- 


• SCALE  THREE  • QUAKERS  • 

• OF  AN  INCH  EQVALS  ONE  - 

• FOOT 


• Small  Letters  aabcd 
c&hyklmnopqnstuv  • 

• wxyz  • for  rapid,  -work 


CAPITALS  ABGDEG 
FHIJKLMNOPQEJT 
UVXWYZ  FEEE-  HAND 


Fig.  10.  Letters  for  Architectural  Office  use. 


483 


14 


ARCHITECTURAL  LETTERING 


Fig.  10  should  be  most  carefully  studied  and  copied,  as  it 
represents  such  actual  letter  shapes  as  are  used  continually  on 


AN  ALPHABET 

£r  ARCHITECTS 

abcdefabi/klmnopg 
rsiuvwxuz  12J4567 
Plan  of  Second  Floor 


ABCPEFCHIJKLM 

NOPQkfTUVWYZ 

A gooS  alphabet  (or 

lettering  plans  &>tc 


Fig.  11.  Single-line  Italic  Letters,  by  Claude  Fayette  Bragdon. 


architectural  drawings,  and  such  as  would,  therefore,  be  of  the 
most  use  to  the  draftsman.  He  should  so  perfect  himself  in  these 
alphabets  that  he  will  have  them  always  at  hand  for  instant  use. 


484 


ARCHITECTURAL  LETTERING 


15 


The  alphabets  of  capital  and  minuscule  one-line  letters 
shown  in  Fig.  11  are  similar  in  general  type  to  those  we  have  just 
been  discussing,  except  that  they  are  sloped  or  inclined  letters 
and  therefore  come  under  the  heading  of  “Italics.”  The  Italic 
letter  is  ordinarily  used  to  emphasize  a word  or  phrase  in  a 
sentence  where  the  major  portion  of  the  letters  are  upright; 


BTPf 


CORINTHIAN  CAP 
FROM  HADRIAN 
BUILDINGS. 

ATHDNS. 


ROSE TTL  FROM 
TEMPLE*  OF  MARS. 
ROME 


CAULICULUSI 
OF  CORINTHIAN 
CAP 


BALUSTER)  3Y  SAN  GALLO 


Fig.  12.  Drawing,  by  Claude  Fayette  Bragdon. 


but  where  the  entire  legend  is  lettered  in  Italics  this  effect  of 
emphasis  is  not  noticeable,  and  a pleasing  and  somewhat  more 
unusual  drawing  is  likely  to  result.  If  it  is  deemed  advisable  to 
emphasize  any  portion  of  the  lettering  on  such  a drawing,  it  is 
necessary  only  to  revert  to  the  upright  form  of  letter  for  that 
portion. 

The  single-line  capitals  and  small  letters  on  the  usual  archi- 
tectural plan  or  working  drawing  are  illustrated  in  Fig.  13,  where 
such  a plan  is  reproduced.  This  drawing  was  not  one  made  spe- 


485 


16 


ARCHITECTURAL  LETTERING 


cially  to  show  this  point,  but  was  selected  from  among  several 
as  best  illustrating  the  use  of  the  letter  forms  themselves,  as  well 
as  good- placing  and  composition  of  the  titles,  both  in  regard  to 
the  general  outline  of  the  plan  and  their  spacing  and  location  in 
the  various  rooms.  It  is  apparent  that  it  is  not  exactly  accurate 
in  the  centering  in  one  or  two  places.  For  instance,  in  the  general 
title,  the  two  lower  lines  are  run  too  far  to  the  right  of  the 
center  line,  and  this  should  be  corrected  in  any  practice  work 
where  these  principles  will  be  utilized.  It  may  be  well  to  say 
that  the  actual  length  of  this  plan  in  the  original  drawing  was 
thirteen  Inches,  and  the  rest  of  it  large  in  proportion.  The 
student  should  not  attempt  to  redraw  any  such  example  as  this 
at  the  size  of  the  illustration.  lie  must  always  allow  for  the  re- 
duction from  the  original  drawing,  and  endeavor  to  reconstruct 
the  example  at  the  original  size,  so  that  it  would  have  the  same 
effect  when  reduced  as  the  model  that  he  follows. 

The  letters  for  notes  and  more  detailed  information  should 
be  much  simpler  and  smaller  than  and  yet  may  he  made  to  accord 
with  the  larger  characters.  Such  a rapid  letter  as  that  shown  in 
Fig.  10,  for  instance,  may  he  used  effectively  with  a severely  clas;- 
sical  title.  Of  course,  no  one  with  a due  regard  for  propriety  or 
for  economy  of  time  would  think  of  using  the  Gothic  small  letter 
for  this  purpose. 

The  portion  of  a drawing  shown  in  Fig.  14  illustrates  an- 
other instance  of  the  use  of  lettering  on  an  architectural  working 
drawing.  The  lettering  defined  by  double  lines  is  in  this  case 
a portion  of  the  architectural  design,  the  two  letters  on  the  pend- 
ant banners  being  sewn  on  to  the  cloth  while  those  on  the  lower 
portion  of  the  drawing  are  square-raised  from  the  background 
and  gilded.  Single-line  capitals  are  used  in  this  example  for  the 
notes  and  information  necessary  to  understand  the  meaning  of 
the  drawing. 

A drawing  of  distinction  should  have  a principal  title  of 
equal  beauty,  such  as  that  shown  in  Fig.  5 or  Fig.  7.  The  ex- 
cellent lettering  reproduced  in  Fig.  12,  from  a drawing  by  Mr. 
Claude  Fayette  Bragdon,  is  a strongly  characteristic  and  in- 
dividual form,  although  based  on  the  same  “skeleton”  idea  as 
the  other  types  of  single-line  lettering  already  referred  to. 


486 


Jicond  - Floor,'  Plan  * 

• One,  - Gjv.gyt>e-r  JncK  vSccrle. 

Fig.  13. 


ARCHITECTURAL  LETTERING 


19 


The  ‘"skeleton”  letter,  formed  on  the  classic  Roman  letter, 
displays  quite  as  clearly  as  does  the  constructive  system  of  Al- 
brecht Diirer,  the  distinctively  square  effect  of  the  Roman  capi- 
tal. The  entire  Roman  alphabet  is  built  upon  this  square  and 
its  units.  The  letters  shown  in  Figs.  22  and  23  are  redrawn  from 
rubbings  of  old  marble  inscriptions  in  the  Roman  Forum,  and 
may  be  taken  as  representative  of  the  best  kind  of  classic  letter 


•ysamr 


BIGELOW 

KENNARD2CO 

GOLDSMITHS 
SILVERSMITHS 
JEWELERS 
IMPORTERS 
MAKERS  OF 
FINE  WATCHES 
AND  CLOCKS 

5ir WASHINGTON  ST 
CORNER  OF  WEST  ST 


Fig.  15.  Advertising  Design,  by  Addison  B.  Le  Boutillier. 


for  incision  in  stone.  The  Diirer  letter,  while  a product  of  a later 
period,  is  fundamentally  the  same,  and  differs  only  in  minor,  if 
characteristic,  details.  However,  for  purposes  of  comparison  it 
will  serve  to  show  the  difference  between  a letter  incised  in  mar- 
ble, or  in  any  other  material,  and  one  designed  for  use  in  letter- 
ing in  black  ink  against  a white  background. 

COMPOSITION. 

After  acquiring  a sufficient  knowledge  of  letter  forms,  the 
student  is  ready  to  begin  the  study  of  “lettering.”  W hile  a 
knowledge  of  architectural  beauty  of  form  is  the  first  essential,  it 


4S9 


20 


ARCHITECTURAL  LETTERING 


BIGELOW,  KENNARD  AND  CO. 
WILL  HOLD,  IN  THE®.  ART 
RO  OMS,  MARCH  Sj  TO  APRIL  6 
INCLUSIVE,  A SPECIAL  EXHIBI- 
TION AND  SALE  OF  GRUEBY 
POTTERY  INCLUDING  THE 
COLLECTION  SELECTED  FOR 
THE  BUFFALO  EXPOSITION 
MDCCCCS 


WASHINGTON  STREET  COR- 
NER OF  WEST  STREET  BOSTON 


Fig.  16.  Cover  Announcement,  by  Addison  B.  Le  Boutillier. 


ARCHITECTURAL  LETTERING 


21 


is  not  the  vital  part  in  lettering,  for  the  composition  of  these  sep- 
arate characters  is  by  far  the  most  important  part  of  the  problem. 

Composition  in  lettering  is  almost  too  intangible  to  define  by 
any  rule.  All  the  suggestions  that  may  be  given  are  of  necessity 
laid  out  on  merely  mathematical  formulae,  and  as  such  are  in- 
capable of  equaling  the  result  that  may  be  obtained  by  spacing 
and  producing  the  effect  solely  from  artistic  experience  and  intui- 
tion. The  final  result  should  always  be  judged  by  its  effect  upon 
the  eye,  which  must  be  trained  until  it  is  susceptible  to  the  slight- 
est deviation  from  the  perfect  whole.  It  is  more  difficult  to  define 
what  good  composition  is  in  lettering  than  in  painting  or  any 
other  of  the  more  generally  accepted  arts,  and  it  resolves  itself 
back  to  the  same  problem.  The  eye  must  be  trained  by  constant 
study  of  good  and  pleasing  forms  and  proportions,  until  it  appre- 
ciates instinctively  almost  intangible  mistakes  in  spacing  and  ar- 
rangement. 

This  point  of  “composition”  is  so  important  that  a legend 
of  most  beautiful  individual  letter  forms,  badly  placed,  will  not 
produce  as  pleasing  an  effect  as  an  arrangement  of  more  awkward 
letters  when  their  composition  is  good.  This  quality  has  been 
so  much  disregarded  in  the  consideration  of  lettering,  that  it  is 
important  the  student’s  attention  should  be  directed  to  it  with 
additional  force,  in  order  that  he  may  begin  with  the  right  feel- 
ing for  his  work. 

An  excellent  example  of  composition  and  spacing  is  shown 
in  Fig.  16,  from  a drawing  by  Mr.  Addison  B.  Le  Boutillier.  The 
relation  between  the  two  panels  of  lettering  and  the  vase  form, 
and  the  placing  of  the  whole  on  the  paper  with  regard  to  its 
margins,  etc.,  are  exceptionally  good,  and  the  rendered  shape  of 
the  vase  is.  just  the  proper  weight  and  color  in  reference  to  the 
weight  and  color  of  the  lettered  panels. 

In  this  reproduction  the  border  line  represents  the  edge  of 
the  paper  upon  which  the  design  itself  was  printed,  and  not  a 
border  line  enclosing  the  panel.  The  real  effect  of  the  original 
composition  can  be  obtained  only  by  eliminating  the  paper  out- 
side of  this  margin  and  by  studying  the  placing  and  mass  of  tin- 
design  in  relation  to  the  remaining  “spot”  and  proportions  of  the 
paper.  Perhaps  the  simplest  and  most  certain  way  to  realize  the 


491 


22 


ARCHITECTURAL  LETTERING 


effect  of  tlie  original  is  to  cut  out  a rectangle  tlie  size  of  this  panel 
from  a differently  colored  piece  of  paper,  and  place  it  over  the 
page  as  a “mask,”  so  that  only  the  outline  of  the  original  design 
will  show  through. 

The  other  example  by  the  same  designer,  shown  in  Fig.  15, 
is  equally  good.  The  use  of  the  letter  with  the  architectural 
ornament,  and  the  form,  proportion,  spacing  and  composition  of 
the  lettering  are  all  admirable. 

The  title  page,  by  Mr.  Claude  Fayette  Bragdon,  shown  in 

Fig.  17,  is  a composition  in- 
cluding the  use  of  many  differ- 
ent types  of  letters ; yet  all  be- 
long to  the  same  period  and 
style,  so  that  an  effect  of  sim- 
plicity is  still  retained.  In 
composition,  this  page  is  not 
unlike  its  possible  composition 
in  type,  but  in  that  case  no  such 
variety  of  form  for  the  letters 
would  be  feasible,  while  the  en- 
tire design  has  an  effect  of 
coherence  and  fusion  which  the 
use  of  a pen  letter  alone  makes 
possible,  and  which  could  not 
be  obtained  at  all  in  typograph- 
ical examples.  The  treatment 
of  the  ornament  incorporated  in 
Fig.  17.  Title  Page,  by  Claude  this  design  should  be  noticed  for 
Fayette  Bragdon.  its  weight  and  rendering,  which 

bear  an  exact  relation  to  the  “color”  of  the  letter  employed. 

In  Fig.  18  is  a lettered  panel  that  will  well  repay  careful 
study.  The  composition  is  admirable,  the  letter  forms  of  great 
distinction — especially  the  small  letters — and  yet  this  example 
has  not  the  innate  refinement  of  the  others.  The  decorative 
panel  at  the  top  is  too  heavy,  and  the  ornament  employed  has 
no  special  beauty  of  form,  fitness,  or  charm  of  rendering  (com- 
pare Figs.  15  and  10),  while  the  weight  of  the  panel  requires 


STORIES 

from  the 
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Curious  and  interefting  Tale* 
Hiftories,  &c;  newly  com- 
pofed  by  Many  Celb- 
b rated  Writers 
and  very  delight- 
ful to  read. 


CHICAGO: 

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and  are  to  be  fold  by  them  at  The 
CaatonBu.ild.iTVi  in  Dearborn  Street 

ibyC 


492 


ARCHITECTURAL  LETTERING 


23 


some  such  over-heavy  border  treatment  as  has  been  used.  Here, 
again,  in  the  slight  Gothic  cusping  at  the  angles  a lack  of  restraint 
or  judgment  on  the  part  of  the  designer  is  indicated,  this  Gothic 
touch  being  entirely  out  of  keeping  with  the  lettering  itself,  and 
only  partially  demanded  by  the  decorative  panel.  Of  course,  it 


Our  First  Exhibit  of 


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POTTERY 

comprising  several 
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will  open  Monday 
March  9th,  1903  in, 
th e,Roo£woocl  ‘Room 
Third  Floor,  Annex 


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COMPANY 


Fig.  18.  Advertising  Announcement. 


is  easy  to  see  that  these  faults  are  all  to  be  attributed  to  an 
attempt  to  attract  and  hold  the  eye  and  thus  add  to  the  value 
of  the  design  as  an  advertisement ; but  a surer  taste  could  have 
obtained  this  result  and  yet  not  at  the  expense  of  the  composition 
as  a whole.  It  is  nevertheless  an  admirable  piece  of  work. 

In  Fig.  19  is  shown  an  example  of  the  use  of  lettering  in 


493 


24 


ARCHITECTURAL  LETTERING 


composition,  in  connection  with  a bolder  design,  in  this  case 
for  a book  cover,  by  Mr.  H.  Van  Buren  Magonigle.  Note  the 
nice  sense  of  relation  between  the  style  of  lettering  employed  and 
the  design  itself,  as  well  as  the  subject  of  the  work.  The  letter 
form  is  a most  excellent  modernization  of  the  classic  Roman 
letter  shape  (compare  Figs.  22  and  23). 


Fig.  19.  Book  Cover,  by  H.  Van  Buren  Magonigle. 

The  student  must  he  ever  appreciative  of  all  examples  of  the 
good  and  bad  uses  of  lettering  that  he  sees,  until  he  can  distin- 
guish the  niceties  of  their  composition  and  appreciate  to  the 
utmost  such  examples  as  the  first  of  these  here  shown.  It  is  only 
by  constant  analysis  of  varied  examples  that  he  can  be  able  to 
distinguish  the  points  that  make  for  good  or  bad  lettering. 


494 


ARCHITECTURAL  LETTERING 


25 


SPACING. 

There  is  a workable  general  rule  that  may  be  given  for 
obtaining  an  even  color  over  a panel  of  black  lettering;  that  is,  if 
the  individual  letters  are  so  spaced  as  to  have  an  equal  area  of 
white  between  them  this  evenness  of  effect  may  be  attained.  But 
when  put  to  its  use,  even  this  rule  will  be  found  to  be  surrounded 
by  pitfalls  for  the  unwary.  Ibis  rule  for  spacing  must  not  be 
understood  to  mean  that  it  applies  as  well  to  composition.  It  does 
not:  it  is,  at  the  best,  but  a makeshift  to  prevent  one  from  eroinir 
far  wrong  in  the  general  tone  of  a panel  of  lettering,  and  must 
therefore  fully  apply  only  to  a legend  employing  one  single  type 
of  letter  form. 

One  with  sufficient  authority  and  experience  to  give  up  de- 
pendence upon  merely  arbitrary  rules,  and  to  rely  upon  his  own 
judgment  and  taste  may,  by  varying  sizes  and  styles  of  letters, 
length  of  word  lines,  etc.,  obtain  a finer  and  much  more  subtle  effect. 

To  acquire  this  authority  in  modern  lettering  it  is  necessary 
to  observe  and  study  the  work  turned  out  today  by  the  best  de- 
signers and  draftsmen,  such  as  the  drawings  of  Edward  Penfield, 
Maxfield  Parrish,  A.  B.  Le  Boutillier  and  several  others.  The 
architectural  journals,  also,  publish  from  month  to  month  beauti- 
fully composed  and  lettered  scale  drawings  by  such  draftsmen  as 
Albert  R.  Ross,  II.  Van  Buren  Magonigle,  Claude  Fayette  Brag- 
don,  Will  S.  Aldrich  and  others,  who  have  had  precisely  the  same 
problem  to  solve  as  is  presented  to  the  draftsman  in  every  new 
office  drawing  that  he  begins. 

Of  course,  the  freer  and  the  further  removed  from  a purely 
Classic  capital  form  is  the  letter  shape  employed  by  the  drafts- 
man, the  less  obliged  is  he  to  follow  Classic  precedent ; but  at  the 
same  time  he  will  find  that  his  drawing  at  once  tends  more  toward 
the  bizarre  and  eccentric,  and  the  chances  are  that  it  will  lose  in 
effectiveness,  quietness,  legibility  and  strength. 

The  student  will  soon  find  that  he  unconsciously  varies  and 
individualizes  the  letters  that  he  constantly  employs,  until  they 
become  most  natural  and  easy  for  him  to  form.  This  insures  his 
developing  a characteristic  letter  of  his  own,  even  when  at  the 
start  he  bases  it  upon  the  same  models  as  have  been  used  by  many 
other  draftsmen. 


495 


26 


ARCHITECTURAL  LETTERING 


niNUSCULE  OR  SHALL  LETTERS. 

In  taking  up  the  use  of  the  small  or  minuscule  letter,  a word 
of  warning  may  be  required.  While  typographical  work  may 
furnish  very  valuable  models  for  composition  and  for  the  individ- 
ual shapes  of  minuscule  letters,  they  should  never  be  studied  for 
the  spacing  of  letters,  as  such  spacing  in  type  is  necessarily  arbi- 
trary, restricted  and  often  unfortunate.  Among  the  lower  case 
types  will  be  found  our  best  models  of  individual  minuscule 
letter  forms,  and  the  Caslon  old  style  is  especially  to  be  com- 
mended in  this  respect;  but  in  following  these  models  the  aim 
must  be  to  get  at  and  express  the  essential  characteristics  of  each 
letter  form,  to  reduce  it  to  a “skeleton”  after  much  the  same 
fashion  as  has  already  been  done  with  the  capital  letter,  rather 
than  to  strive  to  copy  the  inherent  faults  and  characteristics  of 
a type-minuscule  letter.  The  letter  must  become  a “pen  form” 
before  it  will  be  appropriate  or  logical  for  pen  use;  in  other 
words,  the  necessary  limitations  of  the  instrument  and  material 
must  be  yielded  to  before  the  letter  will  be  amenable  to  use  for 
lettering  architectural  drawings. 

The  small  letters  shown  in  Figs.  17,  18  and  20  are  all 
adapted  from  the  Caslon  or  some  similar  type  form,  and  all  ex- 
hibit their  superiority  of  spacing  over  the  possible  use  of  any 
type  letter.  Fig.  20  is  a particularly  free  and  beautiful  example 
indicating  the  latent  possibilities  of  the  minuscule  form  that  are 
as  yet  almost  universally  disregarded.  An  instance  of  the  use 
of  the  small  letter  shown  in  a complete  alphabet  in  Fig.  10,  may 
be  seen  in  Figs.  9 and  13. 

In  lettering  plans  for  working  drawings,  the  small  letter  is 
used  a great  deal.  All  the  minor  notes,  instructions  for  the 
builders  or  contractors,  and  memoranda  of  a generally  unimpor- 
tant character,  are  inscribed  upon  the  drawing  in  these  letters. 
Referring  again  to  Fig.  10,  the  letters  at  the  top  of  the  page  would 
be  those  used  for  the  principal  title,  the  name  of  the  drawing, 
the  name  of  the  building  or  its  owner,  while  the  outline  capitals 
would  be  used  in  the  small  size  beneath  the  general  title,  to  indicate 
the  scale  and  the  architect,  together  with  his  address.  Tn  a small 
building,  or  one  for  domestic  use,  these  same  letters  would  be 
employed  in  naming  the  various  rooms,  etc.,  although  in  an 


496 


ARCHITECTURAL  LETTERING 


27 


elaborate  ornamental  or  public  building,  letters  similar  to  those 
in  the  principal  title  might  be  better  used,  while  the  minuscule 
letter  would  be  utilized  for  all  minor  notes,  memoranda,  direc- 
tions, etc.  By  referring  to  Figs.  3,  5,  7,  8,  9,  13  and  14,  examples 
from  actual  working  drawings  and  plans  are  shown,  which  should 
sufficiently  indicate  the  application  of  this  principle. 

It  must  again  be  emphasized  that  practice  in  the  use  of  these 
forms  combined  together  in  words,  as  well  as  in  more  diffi- 
cultly composed  titles  and  inscriptions  where  various  sizes  and 
kinds  of  letters  are  employed,  is  the  only  method  by  which  the 
draftsman  can  become  proficient  in  the  art  of  lettering;  and 
even  then  he  must  intelligently  study  and  criticise  their  effect 

INTERAVDES 
benoath  tho  Linens  of  SIR. 
R.ICHAR.D  LOVELAGE 
POEM  called  — '"To  Luoafta 
on  going  to  the_>  wars " 
which  saith  : 

Fig.  20.  Pen-drawn  Heading,  by  Harry  Everett  Townsend. 

after  they  are  finished,  as  well  as  study  continually  the  many  good 
drawings  carrying  lettering  reproduced  in  the  architectural  jour- 
nals. For  this  purpose,  in  order  to  keep  abreast  of  the  modern 
advance  in  this  requirement,  he  must  early  learn  to  distinguish 
between  the  instances  of  good  and  bad  composition  and  lettering. 

ARCHITECTURAL  INSCRIPTION  LETTERING. 

The  use  of  a regular  Classic  letter  for  any  purpose  neces- 
sitates the  reversion  to  and  the  study  of  actual  Classic  examples 
for  spacing  and  composition.  In  using  this  letter  in  a pen- 
drawn  design,  certain  changes  must  be  made  in  adapting  it  from 
the  incised  stone-cut  form — which  variations  are,  of  course,  prac- 
tically the  reverse  of  those  required  in  first  adapting  the  letter  for 
use  in  stone.  The  same  letter  for  stone  incision  requires,  in 
addition,  a careful  consideration  of  the  nature  of  the  material, 
and  the  spacing  and  letter  section  that  it  allows.  Also  the  effect 


497 


ABCDEFGHIJKLMN 


Architectural  Capitals. 


ARCHITECTURAL  LETTERING 


29 


of  a letter  in  the  inscription  in  place  must  be  carefully  studied, 
its  height  above  or  below  and  relation  to  the  eye  of  the  observer, 
f he  fact  is  that  the  letter  form  must  in  this  case  be  determined 
solely  by  the  light  and  shadow  cast  by  the  sun  on  a clear,  bright 
day,  or  diffused  more  evenly  on  a cloudy  one.  If  in  an  interior 
location  its  position  in  regard  to  light  and  view-point  is  even  more 
-important,  as  the  conditions  are  less  variable. 

CLASSIC  ROMAN  LETTERS. 

In  any  letter  cut  in  stone,  or  cast  in  metal,  it  is  not  the  out- 
line of  the  letter  that  is  seen  by  the  eye  of  the  observer,  but  the 
shadow  cast  by  the  section  used  to  define  the  letter.  This  at  once 
changes  the  entire  problem  and  makes  it  much  more  complicated. 
In  incising  or  cutting  a letter  into  an  easily  carved  material,  such 
as  stone  or  marble,  we  have  the  examples  left  us  by  the  inventors, 
or  at  least  the  adapters,  of  the  Roman  alphabet.  They  have  gen- 
erally used  it  with  a V-sunk  section,  and  in  architectural  and 
monumental  work  this  is  still  the  safest  method  and  the  one  most 
generally  followed.  One  improvement  has  been  made  in  adapt- 
ing it  to  our  modern  conditions.  The  old  examples  were  most 
often  carved  in  a very  fine  marble  which  allowed  a deep  sinkage 
at  a very  sharp  angle,  thus  obtaining  a well-defined  edge  and  a deep 
shadow.  In  most  modern  work  the  letters  are  cut  in  sandstone 
or  even  in  such  coarse  material  as  granite,  where  sharp  angles  and 
deep  sinkage  of  the  letter-section  is  either  impossible,  or  for  com- 
mercial reasons  influencing  both  contractors  and  stonecutters,  very 
hard  to  obtain.  To  counterbalance  this  fault  a direct  sinkage 
at  right  angles  to  the  surface  of  the  stone  before  beginning  the 
V section  has  been  tried,  and  is  found  to  answer  the  purpose 
very  well,  as  it  at  once  defines  the  edge  of  the  letter  with  a sharp 
shadow.  See  the  two  large  sections  shown  in  the  upper  part  of 
Fig.  31. 

This  section  requires  a letter  of  pretty  good  size  and  width 
of  section,  and,  therefore,  may  be  used  only  on  work  far  removed 
from  the  eye,  as  is  indeed  alone  advisable.  An  inscription  that 
is  to  be  seen  close  at  hand  must  rely  upon  the  more  correct  section 
and  be  cut  as  deeply  as  possible.  For  lettering  placed  at  a great 
height,  an  even  stronger  effect  may  be  obtained  by  making  the 
incised  section  square,  and  sinking  it  directly  into  the  stone. 


499 


so 


ARCHITECTURAL  LETTERING 


Such  pleasant  grading  of  shadows  as  may  be  attained  by  the 
other  method  is  then  impossible,  and  there  are  no  subtle  cross 


Fig.  22.  Classic  Roman  Alphabet. 

From  Marble  Inscriptions  in  the  Roman  Forum. 

lights  on  the  rounding  letters  to  add  interest  and  variety,  but 
the  letter  certainly  carries  farther  and  has  more  strength. 


500 


ARCHITECTURAL  LETTERING 


31 


In  Fig.  21  is  shown  a photograph  from  a model  of  the 
incised  V-sunk  letters  cut  in  granite  on  the  frieze  of  the  Boston 


Fig.  23.  Fragments  of  Classic  Roman  Inscriptions. 


Public  Library.  This  photograph  indicates  the  shadow  effect  that 
defines  the  incised  form  of  the  letter,  and  will  assist  the  student 


32 


ARCHITECTURAL  LETTERING 


somewhat  in  determining  the  section  required  for  the  best  effect 
It  will  be  observed  that  this  letter  is  different  in  character  from 
the  one  used  by  the  same  architects  in  a different  material,  sand- 
stone, shown  in  Fig.  24. 

In  Fig.  22  is  shown  an  alphabet  redrawn  from  a rubbing  of 
Roman  lettering,  and  in  Fig.  23  are  shown  portions  of  Classic 
inscriptions  where  letters  of  various  characters  are  indicated. 
These  letters  were  very  sharply  incised  with  a Y-sunk  section  in 
marble,  and  were  possibly  cut  by  Greek  workmen  in  Rome.  It 
is  on  some  such  alphabet  as  this  that  we  must  form  any  modern 
letter  to  be  used  in  a Classic  inscription  or  upon  a Classic  build- 
ing. These  forms  should  be  compared  with  the  letters  shown  in 
Fig.  24,  on  the  Architectural  Building  at  Harvard,  by  McKirn, 
Mead  & White,  architects,  where  they  were  employed  with  a full 
understanding  of  the  differences  in  use  and  material.  The  Roman 
letter  was  cut  in  marble ; the  modern  letter  in  sandstone.  Both 
were  incised  in  the  V-sunk  section,  but  the  differences  in  material 
will  at  once  indicate  that  the  modern  letter  could  not  have  been 
cut  as  clearly  nor  as  deeply  as  the  old  one.  The  modern  letter 
was  done  a little  more  than  twice  the  original  size  of  the  old  one, 
which  explains  certain  subtleties  in  its  outline  as  here  drawn. 
The  sandstone  being  a darker  material  than  the  marble,  the  letter 
should  of  necessity  be  heavier  and  larger  in  the  same  location, 
in  order  to  “carry”  or  be  distinguishable  at  the  same  distance; 
while  the  Classic  example,  being  sharply  and  deeply  cut  in  a 
beautiful  white  material  which  even  when  wet  retains  much  of  its 
purity  of  color,  would  be  defined  by  a sharper  and  blacker  outline, 
and  therefore  be  more  easily  legible,  other  conditions  being  the 
same,  even  for  a longer  distance.  In  both  these  figures,  the 
composition  of  the  letters  may  be  seen  to  advantage,  as  in  even 
the  Classic  example,  where  they  are  alphabetically  arranged,  they 
are  placed  in  the  same  relation  to  each  other  as  they  held  in  the 
original  inscription.  A complete  alphabet  of  the  letter  shown  in 
word  use  in  Fig.  24,  is  shown  at  larger  size  in  Fig.  25. 

Although  the  lettering  of  the  Italian  Renaissance  period  was 
modeled  closely  after  the  Classic  Roman  form,  it  was  influenced 
by  many  different  considerations,  styles  and  peoples. 


502 


Lettering  from  Harvard  Architectural  Building.  McKim.  Mead  & White,  Architects. 


34  ARCHITECTURAL  LETTERING 


Fig.  25.  Complete  Alphabet. 

Redrawn  from  Inscription  on  Architectural  Building  (See  Fig.  24). 


504 


ARCHITECTURAL  LETTERING. 


35 


505 


36 


ARCHITECTURAL  LETTERING 


Fig.  26.  Fragment  of  Italian  Renaissance  Inscription. 
From  the  Marsuppini  Tomb  in  Florence. 


506 


ARCHITECT!.'  1! AL  LETTERI XG 


37 


ITALIAN  RE- 
NAISSANCE 
LETTERING 
ABCDEFG 
H1JK.LMNE 
OPQRSTU 
VXWYZ 

Fig.  27.  Italian  Renaissance  Lettering. 

Adapted  from  Inscription  shown  in  Fig.  26. 


507 


38 


ARCHITECTURAL  LETTERING 


In  Fig.  26  is  shown  a fragment  of  the  inscription  on  the 
Marsuppini  tomb  at  Florence.  This  outline  letter  was  traced 
from  a rubbing,  and  shows  very  nearly  the  exact  character  of  the 
original,  a marble  incised  letter.  Fig.  27  is  an  alphabet  devised 

TOpaeunx^sf-prpp 

FlTOeffpoMppCfl-wBi 

Fig.  28.  Italian  Renaissance  Inscription  at  Bologna. 

from  this  incised  letter  for  use  as  a pen-drawn  form  and  redrawn 
at  the  same  size.  It  will  be  noticed  that  in  the  letters  shown  in 
the  four  lower  lines  a quite  different  serif*  treatment  has  been 
adopted,  and  certain  of  the  letters,  such  as  the  F/s,  have  been 

fRKPR-9-Olfl 
QOB1-D0  RFHH 
RISD0R6609I 
PSOFlOCRXLai 

Fig.  29.  Italian  Renaissance  Inscription,  Chiaravelle  Abbey  in  Milan. 

“extended”  or  made  wider  in  proportion.  These  variations  are 
such  as  modern  taste  would  generally  advocate,  but  in  the  first 
three  lines  of  this  plate  the  feeling,  serif  treatment  and  letter 
width  of  the  original  have  been  retained ; the  only  change  has 

*Note.  The  “serif”  is  the  short  spur  or  cross  stroke  used  to  define 
and  end  the  main  upright  and  horizontal  lines  of  the  letter. 


508 


ARCHITECTURAL  LETTERING 


39 


H0GO 

Gfi0E 

iann 

CD  D O Q 

QG06 

avcnis 

Z3ZW 

Fig.  30.  Alphabet  of  Uncial  Gothic  Capital  Letters,  16th  Century. 


509 


40 


ARCHITECTURAL  LETTERING 


been  to  narrow  up  the  thin  lines  in  relation  to  the  thick  lines 
to  the  proportions  that  they  should  have  in  a solidly  black  and 
inked-in  letter  form. 

The  two  small  panels,  one  from  a monument  in  Bologna,  and 
one  from  the  Cliiaravelle  Abbey  in  Milan,  Figs.  28  and  29,  show 
a letter  which  was  incised  in  stone  and  follows  the  so-called  uncial 
or  round  form,  with  characteristics  showing  the  probable  influence 
of  the  Byzantine  art  and  period.  These  two  inscriptions  may  be 
compared  with  another  alphabet  showing  the  uncial  character 
when  used  in  black  against'  a white  page,  as  in  Fig.  30.  This 
same  style  of  letter  was  often  used  in  metal,  and  may  be  seen  in 
many  of  the  mortuary  slabs  of  this  and  succeeding  periods. 


Fig.  31.  Inscription  Letter  Sections. 


In  many  of  the  Renaissance  wall  monuments  the  V-sunk 
letter  sections  have  been  filled  with  a black  putty  to  make  the 
letter  very  clear,  and  when  this  falls  out,  as  it  often  does,  the 
V-cut  section  may  still  be  seen  behind  it.  Also  in  many  Italian 
floor  slabs  the  letters  are  either  V-sunk  or  shallow,  square  sinkages 
filled  with  mastic,  or  sometimes  they  are  of  inlaid  marble  of  a 
color  different  from  the  ground.  Again  a V-sunk  letter  section 
sometimes  carries  an  additional  effect  because  it  is  smoothly  cut 


510 


ARCHITECTURAL  LETTERING 


ABCDEFG I 
HljKLMNM 

NPPQQRK 

SVTWXYZ 


Fig.  32.  English  17th  Century  Letters,  from  Tombstones. 


511 


42 


AECHITECTUEAL  LETTEEING 


and  finished  and  the  surface  of  the  stone  is  left  rough,  thus 
obtaining  a different  texture  and  color  effect;  or,  though  more 
rarely,  the  opposite  treatment  may  be  used.  Then,  again,  the 
sides  of  the  letter  sinkage  may  be  painted  or  gilded.  Often  even 
the  shadow  is  painted  into  the  section,  but  this  is  generally  done 
on  interior  cutting  where  there  is  no  direct  light  from  the  sun, 
because  if  direct  sunlight  does  fall  upon  a letter  so  treated,  a very 
amusing  effect  occurs  when  the  shadow  is  in  any  other  position 
than  that  occupied  by  the  painted  representation. 

For  still  further  effects,  raised  lettering  may  be  cut  on  stone 
surfaces.  This  is  more  expensive,  as  it  necessitates  the  more  labor 
in  cutting  back  the  entire  ground  of  the  panel,  but  for  certain 
purposes  it  is  very  appropriate. 

In  such  a letter  the  section  may  be  a raised  V-shape,  or  it 
may  be  rounded  over  to  make  a half  circle  in  section,  as  drawn 
in  Fig.  31.  This  latter  form  is  especially  effective  in  marble, 
but  it  is,  of  course,  very  delicate  and  does  not  carry  to  any 
great  distance.  Its  use  should  be  restricted  to  small  monu- 
mental headstones  or  to  lettering  to  be  read  close  to,  and  below 
the  level  of,  the  eye. 

A raised  letter  is  more  generally  appropriate  for  cast  copper 
and  bronze  tablets,  when  its  section  may  be  a half  round,  a 
raised  V-form,  or  square-raised  with  sharp  corners ; or,  better 
still,  a combination  of  square  and  V-raised  with  a hollow  face. 
See  Fig.  31.  Experience  has  proved  that  this  last-named  section 
produces  the  most  telling  letter  for  an  ordinary  cast-metal  panel. 

Fig.  32  shows  an  alphabet  of  a letter  derived  from  English 
tombstones.  This  letter  was  cut  in  slate  or  an  equally  friable 
material,  and  was  comparatively  shallow.  A certain  tendency 
toward  easing  the  acute  angles  may  be  observed  in  this  alphabet, 
evidently  on  account  of  the  nature  of  the  material  in  which  it 
was  carved  rendering  it  easily  chipped  or  broken. 

In  wood  carving,  a letter  exactly  reversing  the  V-sunk  sec- 
tion with  direct  sinkage,  gives  the  best  effect  for  a raised  letter. 

Every  material,  from  its  nature  and  limitations,  requires 
special  consideration.  A letter  with  many  angles  is  not  adapted 
to  slate,  as  that  material  is  liable  to  chip  and  sliver;  hence  an 


512 


A RCII ITECTU RA L LETTE KING 


Fig.  33.  German  Black  Letters,  from  a Brass. 


513 


44 


ARCHITECTURAL  LETTERING 


uncial  form  with  rounded  angles  suggests  itself  (as  in  Fig.  29), 
and  is,  indeed,  frequently  used. 

It  would  be  quite  impossible  to  take  up  in  detail  the  entire 
list  of  available  materials  and  consider  their  limitations  at  length, 
as  the  task  would  be  endless.  For  the  same  reason,  it  is  not 
possible  to  take  up  each  letter  style  and  consider  its  use  in  stone 
and  other  materials.  Of  course,  a Homan  letter  or  any  other 
similar  form  when  drawn  for  stone-incised  use  must  have  its 
narrow  lines  at  least  twice  as  wide  as  when  drawn  in  ink,  black 
against  a white  background.  (Compare  Figs.  26  and  27.) 

Experience  and  intuition  combined  with  common  sense  will 
go  farther  than  all  the  theory  in  the  world  to  teach  the  limitations 


Fig.  34.  Black-Letter  Alphabet. 


required  by  letter  form  and  material.  The  student,  however, 
should  bear  in  mind  that  it  is  not  necessary  that  he  himself  should 
make  a number  of  mistakes  in  order  to  learn  what  not  to  do.  lie 
may  get  just  as  valuable  information  at  a less  cost  by  observing 
the  mistakes  and  successes  of  others  in  actually  executed  work, 
and  avail  himself  of  their  experience  by  applying  it  with  intelli- 
gence to  his  own  problems  and  requirements. 

GOTHIC  LETTERING. 

Gothic  lettering  is  extremely  difficult,  and  has  little  practical 
use  for  the  architectural  designer  or  draftsman.  It  is  often 
appropriate,  but  it  is  quite  possible  to  get  along  without  employing 
this  form  at  all.  However,  in  case  he  should  require  a letter  of 
this  style,  it  would  be  better  to  refer  him  to  some  book  where  he 
may  study  its  characteristics  more  particularly,  remembering  it 
is  just  as  important  he  should  know  something  of  the  history, 


514 


ARCHITECTURAL  LETTERING 


45 


uses  and  materials  from  which  this  letter  has  been  taken,  as  in 
any  instance  of  the  use  of  the  Roman  form.  Indeed,  it  might  be 


Fig.  35.  Italian  Black  Letters,  after  Bergomensis. 


said,  it  is  even  more  important,  as  the  Gothic  letter  is  more  uni- 
versally misunderstood  and  misapplied  than  the  simpler  Iloman 
letter. 


515 


46 


ARCHITECTURAL  LETTERING 


Fig.  36.  English  Gothic  Text. 


516 


ARCHITECTURAL  LETTERING 


47 


The  alphabet  of  German  black  letters  shown  in  Fig.  35  is 
taken  from  a very  beautiful  example  of  Gothic  black  letter  devised 
bj  Jacopus  Pbillipus  Foresti  (Bergomensis)  and  used  bv  him  in 
the  title  page  of  “De  Claris  Mulieribus,”  etc.,  published*  in  Fer- 
rara in  149  i . Although  Italian,  this  letter  is  as  German  in 
character  as  any  of  the  examples  from  the  pen  of  Albrecht  Diirer. 
A German  black  letter  redrawn  from  a brass  is  shown  in  Fig.  33, 
while  an  English  form  of  Gothic  letter  is  shown  in  Fig.  30. 

In  Fig.  34  is  another  example  of  a black-letter  alphabet. 
The  entire  effect  of  a black-letter  page  depends  upon  the  literal 
interpretation  of  the  title  “black  letter.”  That  is,  the  space 
of  white  between  and  among  the  letters  should  be  overbalanced 
by  the  amount  of  black  used  in  defining  the  letter  form  itself. 

Inasmuch  as  this  letter  is  likely  to  be  used  but  little  by 
architectural  draftsmen,  and  as  it  is  a much  more  difficult  form 
to  compose  than  even  the  Roman  type,  it  seems  better  to  refer 
the  student  to  some  treatise  where  its  characteristics  are  taken 
up  more  thoroughly  and  at  greater  length. 

Any  draftsman  having  occasion  to  use  lettering  to  any  extent 
should  have  some  fairly  elaborate  textbook  always  at  hand  for 
reference. 


EXAMINATION  PLATES. 

In  addition  to  the  following  Examination  Plates  the  student 
is  expected  to  make  careful  reproductions  of  the  lettering  in  this 
Instruction  Paper.  These  plates  need  not  be  sent  to  the  School. 

PLATES  I,  II,  III. 

Draw  the  alphabet,  using  the  same  construction  as  given  in 
Figs.  1 and  2,  and  making  each  letter  two  inches  high.  Put  ten 
letters  on  each  of  the  first  two  plates,  and  on  the  third  arrange  the 
remainder,  including  the  two  forms  of  W given  in  Fig.  2. 


517 


48 


ARCHITECTURAL  LETTERING 


PLATE  IV. 

Make  a careful  reproduction  of  Fig.  10  on  the  left-hand  side 
of  the  plate.  The  letters  should  be  of  the  same  size  as  in  Fig.  10. 
On  the  right-hand  side  of  the  plate  use  the  letter  forms  shown  in 
Fig.  10  and  of  the  same  size,  and  letter  the  following  title,  arrang-. 
ing  the  legend  to  look  well  on  the  plate:  Front  Elevation,  Coun- 

try House  at  Glen  Ridge,  New  Jersey,  Aug.  24,  1903.  David 
Carlson  Mead,  Architect,  No.  5925  State  St.,  Chicago,  111. 

PLATE  V. 

Reproduce  on  this  plate  Figs.  27  and  32  of  the  Instruction 
Paper,  using  letters  of  the  same  size. 

PLATE  VI. 

On  the  left-hand  side  of  this  plate,  copy  the  lettering  shown 
in  Fig.  9,  making  the  letters  at  least  as  large  as  those  in  the  illus- 
tration. On  the  right-hand  side,  following  the  same  style  and 
size,  letter  the  following  title:  Detail  of  Entrance  Porch,  Coun- 
try House  at  Glen  Ridge,  New  Jersey,  Sept.  10,  1903.  David 
Carlson  Mead,  Architect,  No.  5925  State  St.,  Chicago,  111. 

This  plate  to  be  done  in  pencil  only. 

PLATE  VII. 

Using  individual  letter  forms  like  those  shown  in  Figs.  24 
and  25,  letter  the  following  title:  Museum  of  Architecture, 

Erected  in  Memory  of  John  Howard  Shepard,  First  President 
Technology,  Bangor,  Me. 

The  letters  should  be  of  a size  suited  to  the  title;  the  title 
should  occupy  five  lines. 

All  plates  except  Plate  VI  should  be  inked  in.  The 
student  should  first  lay  out  his  lettering  in  pencil  in 
order  to  obtain  the  proper  spacing  of  the  center  line 
on  his  page  or  panel.  He  should  also  place  guide  lines 
in  pencil  at  the  top  and  bottom  of  his  lettering  for  both 
capitals  and  small  letters. 

The  plates  should  be  drawn  on  a smooth  drawing 
paper  11  inches  by  15  inches  in  size.  The  panel  inside 
dhe  border  lines  should  be  10  inches  by  14  inches.  For 
best  work  Strathmore  (smooth  finish)  or  Whatman’s 
hot-pressed  drawing  paper  is  recommended. 

The  date,  the  student’s  name  and  address,  and  the 
plate  number  should  be  lettered  on  each  plate  in  one- 
line  letters  such  as  are  shown  in  Fig.  10. 


518 


GENERAL  INDEX 


irsuDEzx: 


The  Cyclopedia  of  Drawing  is  inn.de  up  of  the  regular  instruction 
papers  from  courses  in  the  American  School  of  Correspondence  at 
Armour  Institute  of  Technology.  The  titles  and  page  numbers  of  these 
instruction  papers  are  given  as  running  headings  at  the  top  of  the  pages. 

The  page  numbers  referred  to  in  the  Index 
will  be  found  at  the  bottom  of  the  pages. 


Page 

Adjustable  T-square  12 

Angles,  measurement  of  5G 

Apparent  distortion  324 

Architectural  lettering  473-513 

classic  letters  474 

classic  renaissance  letters  476 

classic  Roman  letters  499 

composition  489 

Diirer  letter  489 

early  English  letters  511 

English  Gothic  516 

Gothic  lettering  514 

inscription  lettering  497 

Italian  Renaissance  lettering  507 

Italic  letters  485 

office  lettering  473 

plates  517-518 

“skeleton”  letter  ■ 489 

small  letters  496 

spacing  495 

uncial  Gothic  capital  509 

Assembly  drawing  154 

Auxiliary  line  of  measures  279 

Auxiliary  planes  198 

Beam  compasses  25 

Black  print  solution  155 

Blue  print  solution  155 

Blue  printing  153 

Bow  pen  20 

Bow  pencil  20 

Brushes  and  paper  for  rendering  457 


Note.— For  page  numbers  see  foot  of  pages 


Camera  and  eye 

Page 

342 

Color  combination 

457 

Colors 

458 

Combination  of  color 

457 

Compasses 

16 

beam 

25 

Composition  in  lettering 

489 

Cross  hatching 

374 

Curves  in  perspective  drawing 

319 

Definitions 

drawing 

341 

geometrical 

.51-64 

ray  of  light 

174 

shade 

173 

shade  line 

174 

shadow 

173 

Umbra 

174 

Developments 

112 

, 163 

cone 

111 

cylinder 

116 

intersection  of  pyramid 

120 

rectangular  prism 

113 

right  prism 

113 

Directions  of  shade  lines 

375 

Dividers 

19 

Drawing 

definition  of 

341 

restraint  in 

343 

Drawing  board,  mechanical 

drawing 

9 

Drawing  paper,  mechanical 

drawing 

7 

523 


2 


INDEX 


Drawing  pen 

Page 

20 

Geometrical  definitions 

Page 

Drawing  plates,  general  directions  for 

373 

polygons 

54 

Elementary  problems  in  perspective 

271 

pyramids 

58 

Ellipse,  actual  size  of 

111 

quadrilaterals 

53 

English  Gothic  text  letters 

516 

solids 

57 

English  letters,  early 

511 

spheres 

60 

Erasers 

10 

surfaces 

52 

Eye  and  camera 

342 

triangles 

52 

Five  axioms  of  perspective 

255 

Geometrical  problems,  mechanical 

Forms  of  letters,  derivation  of 

475 

drawing 

65-89 

Free-hand  drawing 

341 

-404 

Gothic  lettering 

143 

first  exercises 

349 

-354 

Holding  the  pencil 

348 

circles  and  ellipses 

350 

Horizon 

255 

free-hand  perspective 

352 

Incised  letters 

478 

learning  to  see 

344 

Ink 

22 

straight  lines 

349 

Inking  37, 

42,  47 

testing  with  the  slate 

353 

Inscription  lettering 

497 

tracing  on  the  slate 

352 

Instruments  in  mechanical  drawing  7 

materials 

346 

beam  compasses 

25 

plates 

379 

-404 

bow  pen 

20 

value  of  to  an  architect 

341 

bow  pencil 

20 

Free-hand  lettering 

168 

compasses 

16 

Free-hand  perspective 

355' 

-376 

dividers 

19 

appearance  of  equal  spaces 

359 

drawing  board 

9 

center  of  ellipse 

363 

drawing  pen 

20 

concentric  circles 

364 

erasers 

10 

cone 

362 

irregular  curve 

24 

cylinder 

360 

pencils 

10 

foreshortened  planes  and  lines 

356 

protractor 

23 

frames 

364 

scales  ’ 

23 

horizon  line  or  eye  level 

355 

thumb  tacks 

9 

horizontal  circle 

357 

triangles 

13 

parallel  lines 

358 

T-square 

11 

prism 

360 

Intersection 

107 

regular  hexagon 

363 

Intersection  of  plane  with  solids 

108 

square 

358 

Irregular  curve 

24 

triangle 

359 

Isometric  axes 

127 

General  directions'  for  drawing  objects 

366 

Isometric  and  oblique  projection 

164 

Geometrical  definitions 

Isometric  projection 

125 

angles 

52 

bench 

137 

circles 

55 

box 

132 

cones 

59 

cube 

125 

conic  sections 

61 

Italic  letters 

485 

cylinders 

59 

Kind  of  drawing 

407 

lines 

51 

Learning  to  see 

344 

odontoidal  curves 

63 

Letter  forms 

474 

Note.— For  page  numbers  see  foot  of  pages. 


524 


INDEX 


Lettering  25-29, 

Page 
142,  16S 

Mechanical  drawing 

Page 

architectural 

473 

-518 

lettering 

142 

on  arc  of  a circle 

148 

line  shading 

140 

capital  letters 

28 

materials 

7 

free-hand 

168 

oblique  projections 

137 

Gothic 

143 

orthographic  projections 

91 

Gothic  capitals 

26 

pencilling 

31 

lower-case  letters 

28, 

145 

plates 

29-48 

mechanical 

25 

shade  lines 

103 

Roman 

143 

tracing 

150 

Roman  capitals 

26 

Minuscule 

496 

spacing  in 

147 

Misuse  of  tests 

369 

Light  and  shade 

370, 

412 

Notation,  perspective  drawing 

269 

color  of  material 

415 

Oblique  lines,  vanishing  points  of 

289 

form  drawing 

370 

Oblique  projection 

137 

lighting 

414 

cube 

138 

principality  or  accent 

417 

line  shading 

140 

shadows  only 

416 

Office  lettering 

473 

value  drawing 

370 

One-point  perspective 

302 

values 

412 

Orthographic  projection 

91 

Line  shading 

140 

Outline 

344 

Line  work  in  rendering 

408 

Parallel  perspective 

302 

free  lines 

411 

Pen  and  ink,  rendering  in 

407-437 

method 

410 

Pencil  work 

419 

quality  of  line 

408 

Pencilling  31,  32, 

41,  43 

vertical  lines 

411 

Pencil  rendering 

419 

Lines  of  measures 

279 

Pencils 

10 

Lower-case  letters 

145 

Perspective  drawing 

249-337 

Materials  for  free-hand  drawing 

346 

axioms 

257 

paper 

348 

curves 

319 

pencils 

346 

definitions 

249 

Materials  in  mechanical  drawing 

7 

lines  of  measures 

279 

Materials  for  pen  rendering 

408 

notation 

269 

Measure  lines  in  perspective 

279, 

311 

parallel  perspective 

302 

Measure  point  in  perspective 

311 

perspective  plan  method 

309 

Measurement  of  angles 

56 

planes  of  projection 

259 

Mechanical  drawing 

7- 

-168 

plates 

329-337 

conic  sections 

61 

problems  in  perspective 

development 

112 

point 

271 

drawing  paper 

7 

line 

272 

geometrical  definitions 

51 

L-64 

vanishing  point 

273 

geometrical  problems 

65-89 

revolved  plan  method 

274 

ink 

22 

vanishing  point  diagram 

301 

instruments 

7 

vanishing  point  of  oblique  line 

289 

intersections 

107 

Perspective  free-hand 

355 

isometric  projection 

125 

Perspective  of  a house 

285 

Note.— Fop  page  numbers  see  foot  of  pages. 


525 


4 


INDEX 


Perspective  of  interior 

Page 

304 

Restraint  in  drawing 

Page 

343 

Perspective  plan,  method  of 

309 

Revolved  plan,  method  of 

274 

Perspective  of  a point 

261 

Roman  lettering 

143 

Perspective  projection 

259 

Scales 

23 

Perspective  of  steps 

305 

Shade  lines 

103,  140 

Picture  plane 

250 

directions  of 

375 

Plane  of  the  horizon 

255 

orthographic  projection 

103 

Planes  of  light 

203 

sphere 

204 

Planes  of  projection 

259 

Shades  and  shadows 

173-248 

Plates,  mechanical  drawing  25-48, 

156-168 

auxiliary  planes 

19S 

Point  of  sight 

250 

chimney  on  a sloping  roof 

187 

Position 

349 

cone 

194 

Projection  planes 

259 

construction 

20S 

Projections,  mechanical  drawing 

91 

definitions 

173 

developments 

112 

hand  rail 

191 

intersection 

107 

notation 

175 

isometric 

125 

object 

184 

oblique 

137 

oblique  cylinder 

196 

orthographic 

91 

pedestal 

187 

profile  plane 

97 

planes  of  light 

203 

shade  lines 

103 

polyhedron 

182 

Ray  of  light 

175 

prism 

183 

Rendering  in  pen  and  ink 

407-437 

problems 

176-217 

accent 

417 

right  cylinder 

19£ 

brushes  and  paper 

457 

short  method  construction 

208-211 

kinds  of  drawing 

407 

cylinder 

212 

light  and  shade 

412 

intrados 

214 

line  work 

408 

line 

209 

manipulation 

457 

point 

208 

materials 

40S 

right  cylinder 

213 

pencil  work  ’ 

419 

sphere 

215 

plates  for  practice 

425-437 

spherical  hollow 

215 

Rendering  in  wash 

441-470 

torus 

216 

materials 

441 

vertical  line 

214 

method  of  procedure 

442 

in  spherical  hollow 

198 

distinction  between  planes  454 

Shading,  varieties  of 

374 

graded  tints 

452 

Shadow  of 

handling  the  brush 

444 

given  line 

178 

inking  the  drawing 

442 

given  plane 

181 

laying  washes 

444 

lines 

178 

preparing  the  tint 

443 

pediment  mouldings 

204 

rendering  elevations 

450 

planes 

181 

rendering  sections  and  plans  452 

points 

176 

stretching  paper 

442 

scotia 

200 

plates 

463-470 

solids 

18? 

water  color  hints 

454-460 

Skeleton  letters 

480 

Note.-  For  page  numbers  see  foot  of  pages. 


526 


INDEX 


Page 


Small  letters  490 

Spacing  in  lettering  495 

Station  point  250 

T-square  11 

Testing  drawing  by  measurement  367 
Thumb  tacks,  mechanical  drawing  9 

Tracing  150 

Triangles  13 

Tube  and  pan  colors  454 

Value  of  free-hand  drawing  to  an 

architect  341 

Values  of  light  and  dark  371 

Value  scale  371 

how  to  make  373 


Page 


Value  scale 

how  to  use  373 

Vanishing  point  diagram  301 

Vanishing  point  of  lines  252 

Vanishing  point  of  oblique  lines  289 

Vanishing  trace  251 

Varieties  of  shading  374 

Visual  element  253 

Visual  plane  253 

Visual  rays  of  light  249 

Water  color  hints  451 

Water  color  rendering  459 

Water  color  sketching  460 


Note.— For  page  numbers  see  foot  of  pages. 


5 2Ti 


OFFICES,  AMERICAN  SCHOOL  OF  CORRESPONDENCE. 


THE  FOLLOWING  PAGES  ARE  TAKEN  FROM 
THE  BULLETIN  OF  THE  AMERICAN  SCHOOL  OF 
CORRESPONDENCE  AT  ARMOUR  INSTITUTE  OF 
TECHNOLOGY,  CHICAGO. 

OTHER  COURSES  OFFERED  ARE!  HEATING, 
VENTILATING  AND  PLUMBING;  CIVIL,  ELECTRI- 
CAL, MECHANICAL,  STATIONARY,  LOCOMOTIVE, 
AND  MARINE  ENGINEERING;  ELECTRIC  WIRING; 
REFRIGERATION;  TELEPHONY;  TELEGRAPHY,  TEX- 
TILES, INCLUDING  KNITTING;  THE  MAUFACTURE 
OF  COTTON  AND  WOOLEN  CLOTH , TEXTI  LE  CHEM- 
ISTRY, DYEING,  FINISHING,  AND  DESIGN;  ALSO 
COLLEGE  PREPARATORY,  FITTING  STUDENTS 
FOR  ENTRANCE  TO  ENGINEERING  COLLEGES. 

THE  COLLEGE  PREPARATORY  COURSE  PRAC- 
TICALLY COVERS  THE  WORK  OF  THE  SCIENTIFIC 
ACADEMY  OF  ARMOUR  INSTITUTE  OF  TECH- 
NOLOGY, AND  IS  ACCEPTED  AS  FULFILLING  THE 
REQUIREMENTS  FOR  ENTRANCE  TO  THE  COL- 
LEGE OF  ENGINEERING  OF  THAT  INSTITUTION- 
THE  BULLETIN  OF  THE  SCHOOL,  GIVING 
COMPLETE  SYNOPSIS  OF  THE  ABOVE  COURSES, 
MAY  BE  HAD  ON  REQUEST 


• GREEJGDORIC-AND  ‘ I ON  I C 


AH,  TO  BUILD,  TO  BUILD! 

THAT  IS  THE  NOBLEST  ART  OF  ALL  THE  ARTS. 
PAINTING  AND  SCULPTURE  ARE  BUT  IMAGES, 

ARE  MERELY  SHADOWS  CAST  BY  OUTWARD  THINGS 
ON  STONE  OR  CANVAS,  HAVING  IN  THEMSELVES 
NO  SEPARATE  EXISTENCE.  ARCHITECTURE, 
EXISTING  IN  ITSELF,  AND  NOT  IN  SEEMING 
A SOMETHING  IT  IS  NOT,  SURPASSES  THEM 
AS  SUBSTANCE  SHADOW. 

Henry  Wadsworth  Longfellow . 


'<STELE>  CRESTS 


SPECIMEN  PAGE  FROM  INSTRUCTION  PAPER  ON  THE  ORDERS. 


DEPARTMENT  OF 

ARCHITECTURE 


COURSES 

COMPLETE  ARCHITECTURE 

ARCHITECTURAL  ENGINEERING 

CONTRACTORS’  AND  BUILDERS’ 

ARCHITECTURAL  DRAWING 
CARPENTERS’ 


ARCHITECTURE 

HE  courses  in  Architecture  are  planned  to  cover  the 
actual  problems  arising  in  daily  work.  They  offer 
young  men  in  the  architect’s  office  or  in  the  con- 
tractor’s employ  an  opportunity  to  obtain  practical 
information  which  ordinarily  could  be  acquired  only 
: after  long  apprenticeship.  The  instruction  is  of  im- 
mediate value  to  carpenters,  contractors  and  others  engaged  in  build- 
ing, as  great  stress  is  laid  on  the  practical  as  well  as  the  artistic  side 
of  the  work.  The  courses  offer  experienced  draftsmen  and  practicing 
architects  an  opportunity  to  make  up  deficiencies  in  their  early  pro- 
fessional training.  The  instruction  in  Heating,  Ventilating,  Plumb- 
ing, Gas  Lighting,  Wiring, — Electricity  and  Steam  as  applied  to  power 
and  light— is  such  as  to  enable  an  architect  to  obtain  an  intelligent 
knowledge  of  subjects  which  are  of  growing  importance  in  the  plan- 
ning of  large  buildings. 

The  instruction  comprises  Mechanical  Drawing,  Descriptive 
Geometry  as  used  in  framing,  Isometric  and  Perspective  Drawing, 
Shades  and  Shadows,  Free-hand  Drawing,  Pen  and  Ink  Rendering, 
and  the  conventional  methods  of  making,  figuring,  lettering  and  ren- 
dering plans,  elevations,  sections  and  details.  -The  student  is  taught 
the  theory  of  the  design  of  columns,  beams,  girders  and  trusses. 
Building  Materials,  Building  Construction . and  Details,  including 
framing”  sheet-metal  work,  fireproofing,  wiring,  piping,  heating  and 
ventilating  systems,  Building  Superintendence,  Specifications  and 
Contracts,  Building  Laws  and  Permits,  and  general  office  practice 

are  also  discussed.  . , , • • 

In  connection  with  Architectural  History,  instruction  is  given  in 

History  of  Ornament,  Ornamental  Design,  followed  by  .a  car®fll^s^lldy 
of  the  fundamental  principles  of  design  beginning  with  the  Orders. 
These  principles  are  impressed  upon  the  student  by  a sen<  - of  interest- 
ing problems  in  architectural  design. 


533 


COMPLETE  ARCHITECTURE 


Prepared  for  Draftsmen,  Designers,  Architects,  Architectural  En- 
gineers, Landscape  Architects,  Building  Superintendents,  Quantity  Sur- 
veyors, Clerks  of  Building  Works,  Inspectors,  Contractors  and  Builders, 
Masons,  Plasterers,  Carpenters  and  Joiners,  Heating  and  Ventilating  En- 
gineers, Steam  Fitters,  Salesmen  of  Building  Materials,  Real  Estate 
Agents,  Instructors,  Students  and  others. 


INSTRUCTION  PAPERS  IN  THE  COURSE 


Arithmetic  Part  I. 

Arithmetic  Part  II. 

Arithmetic  Part  III. 

Elementary  Algebra  and  Men- 
suration. 

Algebra  Part  I. 

♦Algebra  Part  II. 

Geometry. 

♦Trigonometry  and  Logarithms. 
Mechanical  Drawing  Part  I. 
Mechanical  Drawing  Part  II. 
Freehand  Drawing. 

Mechanical  Drawing  Part  III. 
Mechanical  Drawing  Part  IV. 
Architectural  Lettering. 

Shades  and  Shadows. 

Perspective  Drawing. 
Architectural  Drawing. 
Rendering. 

Study  of  the  Orders  Part  I. 

Study  of  the  Orders  Part  II. 
Study  of  the  Orders  Part  III. 
History  of  Architecture. 
Practical  Problems  in  Design. 


Building  Superintendence  Part  I. 
Building  Superintendence  Part  II. 
Working  Drawings. 

Building  Materials. 

Strength  of  Materials  Part  I. 
Strength  of  Materials  Part  II. 
Foundations. 

Masonry. 

Carpentry  and  Joinery  Part  I. 
Carpentry  and  Joinery  Part  II. 
Stair  Building. 

Statics. 

Steel  Construction  Part  I. 

Steel  Construction  Part  II. 

Steel  Construction  Part  III. 
Fireproofing. 

Contracts  and  Specifications. 
Legal  Relations. 

Heating  and  Ventilation  Part  I. 
Heating  and  Ventilation  Part  II. 
Heating  and  Ventilation  Part  III 
Plumbing  Part  I. 

Plumbing  Part  II. 


♦Optional. 


534 


ISP 


SPECIMEN  PAGE  FROM  INSTRUCTION  PAPER  ON  TUE  ORDERS. 


SPECIMEN  PAGE  FROM  INSTRUCTION  PAPER  ON  WORKING  DRAWINGS. 


SYNOPSIS  OF  COURSE 

MATHEMATICS 


ARITHMETIC:  Units:  Numbers;  N dj. 

vision;  Factoring;  Cancellation;  Fractions:  Decimals:  Symbols  of  Aggregation;  per- 

centage; Denominate  Numbers;  Tables  of  Linear  and  Square 
Measure:  Tables  of  Weights;  Involution;  Evolution;  Square 
Root;  Cube  Root;  Roots  of  Fractious;  Ratio;  Proportion. 

ELEMENTARY  ALGEBRA:  Use  of  Letters;  Addition;  Sub- 

traction; Multiplication;  Division;  Cancellation;  Equations; 

Transportation  Finding  Value  of  Unknown  Quantities. 

MENSURATION:  Lines;  Angles:  Polygons;  Circles:  Sectors 

and  Segments.  Measurement  of  Angles;  Triangles;  Rect- 
angles; Trapezoids;  Hexagons:  Circles;  Volumes  and  Sur- 
faces of  Prisms;  Cylinders;  Pyramids;  Cones:  Frustums; 

Sphere.  Practical  Problem:  Measurement  of  Steam  Space  in 

a Horizontal  Multitubular  Boiler. 


ALGEBRA 


EXPRESSIONS:  Symbols:  Coefficients  and  Exponents:  Symbols  of  Relation;  Symbols  of 

Abbreviation:  Positive  and  Negative  Terms:  Monomial;  Binomial;  Trinomial:  Poly- 

nomials; Similar  Terms.  Finding  Numerical  Value  by  Substitution.  Finding  Values 
of  Unknown  Quantities. 

FUNDAMENTAL  PROCESSES:  Addition;  Subtra<  Multiplica- 

tion; Division;  Formulae;  Factoring;  Highest  Common  Factor;  Lowest  Common 
Multiple. 

FRACTIONS:  Fractions  and  Integers;  Reduction  of  Fractions  t<>  Lowest  Terms;  Reduc- 

tion of  Fractions  to  Entire  or  Mixed  Quantities;  Reduction  of  Mixed  Quantities  to 
Fractions:  Reduction  of  Fractions  to  Lowest  Common  Denominator:  Addition  and  Sub- 

traction of  Fractions;  Multiplication  and  Division  of  Fractions;  Complex  Fractions. 

SIMPLE  EQUATIONS:  Transposition;  Solution  of  Simple  Equations;  S lntl 

tions  Containing  Fractions:  Literal  Equations;  Equations  Involving  Decimals;  Equa- 
tions Containing  Two  Unknown  Quantities:  Elimiuation  by  Addition,  Subtraction, 

Substitution  and  Comparison. 

INVOLUTION  AND  EVOLUTION:  Monomials  and 

Polynomials;  Squares.  Cubes  and  Higher  Powers. 

The  Radical  Sign;  Theory  of  Exponents:  Radicals; 

Reduction  of  Radicals  to  Simplest  Form;  Addition, 

Subtraction,  Multiplication  and  Division  of  Radi- 
cals. Involution  and  Evolution  of  Radicals.  Irra- 
tional Denominators;  Approximate  Values. 

IMAGINARY  QUANTITIES:  Multiplication  and  Division  of  Imaginary  Quantities.  Quad- 

ratic Surds. 

EQUATIONS:  Solution  of  Equations  Containing  Radicals.  Pure  and  Affected  Quadratic 

Equations;  Simultaneous  Equations  Involving  Quadratics. 

RATIO  AND  PROPORTION:  Alternation;  Inversion;  Composition;  Divi 

PROGRESSION:  Arithmetical  and  Geometrical. 

BINOMIAL  THEOREM:  Formulae;  Positive  Integers;  Finding  Terms  in  an  Expansion. 


GEOMETRY 


DEFINITIONS:  Principles;  Axioms:  Abbreviations.  Angles:  Acute;  Obtuse;  Comple- 

mentary; Supplementary;  etc.  Parallel  Lines;  Axioms. 

FUNDAMENTAL  THEOREMS:  Plane  Figures:  Polygons:  Equilat- 

, eral  and  Equiangular.  Quadrilaterals;  Circles;  Measurements  “f 

Angles;  Similar  Figures;  Trapezium;  Trapezoid; 
gram:  Rectangle;  Square;  Rhomboid;  Rhombus. 

Proportion. 

Division. 

SIMILAR  POLYGONS:  Definitions.  Theorems.  Areas  of  Miscel- 
laneous Figures;  Equivalent  Polygons:  Rectangles,  Parallelo- 

grams. 

Twenty-nine  Problems  in  Construction  of  Plane  Figures. 


C 

K 


Terms;  Alternation; 
The  Circle:  Theorems; 


Parallelo- 
Ratio  and 
Inversion;  Composition  and 
Area;  Circumference,  etc. 


PROBLEMS  OF  CONSTRUCTION: 


537 


TRIGONOMETRY  AND  LOGARITHMS 

TRIGONOMETRY:  Definitions;  Functions  of  Acute  Angles;  Measurement  of  Angles; 

Complementary  Functions.  Theorems  Connecting  the  Different  Functions  of  an  Angle. 
FUNCTIONS:  From  One  Function  of  an  Angle  to  Find  the  Other  Functions.  Functions 

of  45  degrees,  30  degrees  and  60  degrees.  Trigonometric  Functions  of  Any  Angle. 
Positive  and  Negative  Angles;  The  Four  Quadrants.  Functions  of  0 degrees,  90  de- 
grees, 180  degrees  and  270  degrees.  Angles  and  Triangles. 

LOGARITHMS:  Nature  and  Use  of  Logarithms;  Logarithms  of 

a Product,  a Fraction,  a Power,  a Root.  Solutions  of  Arith- 
metical Problems  by  Logarithms. 

TRIANGLES:  Right  Triangles:  Solution  by  Natural  Functions; 

Solutions  by  Logarithms;  Areas.  Oblique  Triangles:  Solu- 

tion by  Breaking  up  into  Right  Triangles;  Areas. 

EXERCISES:  Length  of  Belt  over  two  Pulleys;  Stress  in  Rods 

forming  an  Acute  Angle. 


DRAWING 

INSTRUMENTS  AND  MATERIALS:  Drawing  Paper;  Board;  Pencils;  T-Squares;  Tri 

angles;  Compasses;  Line  Pens;  Scales;  Irregular  Curves;  Lettering  Plates;  Exercises 
GEOMETRICAL  DRAWING:  Lines;  Angles;  Triangles;  Parallelograms;  Pentagon;  Hexa 

gon;  Circles;  Measurement  of  Angles.  Prisms 
Pyramids;  Cylinders;  Cones;  Spheres.  Ellipse; 
Parabola;  Hyperbola;  Twenty-eight  Problems  in 
Geometrical  Drawing. 

PROJECTIONS:  Orthographic:  Plan  and  Elevation; 

Projection  of  Points,  Lines,  Surfaces  and  Solids.« 
Third  Plane  of  Projection;  True  Length;  Inter- 
section of  Planes  with  Cones  and  Cylinders;  De- 
velopment of  Prisms,  Cylinders,  Cones,  etc.  De- 
velopment of  Elbow.  Isometric:  Isometric  Axes; 

Cube;  Cylinder;  Directions  of  Rays  of  Light. 
Oblique  Projections:  Shade  Lines;  Co-ordinates. 

Isometric  of  House,  etc. 

WORKING  DRAWINGS:  Lines.  Location  of  Views;  Cross-Sections;  Crosshatching; 

Dimensions;  Finished  Surfaces;  Material;  Conventional  Representations  of  Screw 
Threads.  Bolts  and  Nuts.  Threads  in  Sectional  Pieces;  Broken  Shafts,  Columns, 
etc.  Tables  of  Standard  Screw  Threads,  Bolts  and  Nuts.  Scale  Drawing;  Assembly 
Drawing;  Blue  Printing;  Formulas  for  Solutions  for  Blue-Print  Paper. 

PERSPECTIVE  DRAWING:  Station  Point;  Picture  Plane; 

Ground  Line;  Horizon;  Line  of  Measures;  Axis;  Vertical 
Trace;  Horizontal  Trace;  Bird’s-eye  View;  Worm’s-eye 
View;  Vanishing  Points.  Projections:  Planes;  Notation. 

Problems  Involving  Perspective  of  Points,  Lines  and  Planes. 

Revolved  Plan;  Lines  of  Measure;  Diagrams;  Revolved  Plan 
and  Elevation;  Systems  of  Lines  and  Planes;  Visual  Ray; 

Perspective  Diagram;  Method  of  Perspective  Plan;  Curves; 

Apparent  Distortion;  Choice  of  Position  of  Station  Point. 

Plates. 

SHADES  AND  SHADOWS:  Principles  and  Notation;  Shadows  of 

Points,  Lines  and  Planes.  Co-ordinate  Planes;  Lines  on 
More  Than  One  Surface.  Choosing  Ground  Line  Problems: 

Shadows  of  Prism;  Pedestal;  Chimney  on  Roof;  Rail  on 
Steps;  Cone:  Cylinder.  Auxiliary  Planes;  Shadow  of 

Spherical  Hollow;  Shadow  of  Scotia.  Planes  of  Light; 

Shadow  of  a Sphere;  Shadow  on  Pediment  Moulding.  Short  Methods:  Shadows  of 
Points;  Lines  Parallel  and  Perpendicular  to  Co-ordinate  Planes.  Shadows  on  Inclined 
Planes;  on  Planes  Parallel  and  Perpendicular  to  Co-ordinate  Planes.  Shade  and 
Shadow  of  Cylinder;  of  Line  Moulding;  on  Intrados  of  Circular  Arch;  of  Spherical 
Hollow  and  Niche;  of  Sphere;  of  Torus. 

RENDERING:  Pen  and  Ink:  Materials  Used,  Examples  Showing 

Common  Faults,  Values,  Lighting,  Rendering  by  Shadows  Only, 
Accent,  Pencil  Work,  Suggestions  and  Cautions,  Examples  of 
Drawings  with  Criticisms. 

WASH  DRAWINGS:  Inking  the  Drawing;  Preparing  the  Tint; 

Handling  the  Brush;  Laying  on  the  Washes;  Tinting  Eleva- 
tions, Sections  and  Plans;  Graded  Tints;  Distinction  between 
different  Planes;  French  Method. 

WATER-COLOR  HINTS  FOR  DRAFTSMEN:  List  of  Colors; 

Manipulation;  Brushes  and  Paper;  Combinations  of  Color; 
Primary,  Secondary  and  Complementary  Colors;  Water-color 
Rendering;  Water-color  Sketching. 

FREE  HAND  DRAWING:  Paper;  Pencils;  Drawing  Board. 

Difference  between  a Drawing  and  a Photograph.  Lines  and 
Surfaces.  Flat  Ornament:  Anthemia;  Frets;  Mosaics; 

Stained  Glass;  All  Over  Patterns.  Light  and  Shade:  Value 

Scale;  Form  Drawing;  Point  of  View;  Value  Drawing.  Geo- 
Working  Drawings.  metric  Solids.  Carved  Ornament:  Rosettes;  Greek,  Roman 

and  Byzantine  Acanthus;  Ionic;  Corinthian  and  Gothic  Capitals;  Renaissance  Pilaster. 
ARCHITECTURAL  LETTERING:  Office  Lettering;  Purpose;  Relative  Sizes  and  Shapes 

of  Letters  for  Titles;  Forms  and  Proportions  of  Various  Alphabets.  Skeleton  Letters. 
Composition  and  Spacing:  Title  Page;  Lettering  Plans  and  Working  Drawings.  In- 

scription Lettering.  Letters  for  Stone;  Shadows;  Cast  Letters;  Raised  Letters; 
Examples  of  Lettering;  Gothic;  Roman.  Examination  Plates. 


fife 


538 


SPECIMEN  PAGE  FROM  INSTRUCTION  PAPER  ON  THE  ORDERS. 


W'  o,  " or  " -1«V»V 


d 


-d 


FRONT"  FLE.VAT10JV 


ARCHITECTURE 


HISTORY  OF  ARCHITECTURE:  Ancient  Architecture;  Egyptian;  Mzyrtan;  G. 

Done,  Ionic  and  Corinthian  Orders.  Greek  Tombs  and  Theatres;  The  Acropolis; 
Roman  Architecture:  Temples;  Theatres;  Tombs;  Triumphal  Arches;  Medieval  Arehl- 


teeture:  Romanesque;  Gothic;  English  Gothic;  Early  French 

Styles;  Renaissance;  Italian;  French;  Spanish;  German; 
English.  Classic.  European  Architecture.  American  Ar- 
chitecture: Colonial;  Residences;  Public  Buildings;  Churches: 
Commercial  Architecture. 

STUDY  OF  THE  ORDERS:  The  Five  Orders:  Tuscan;  Doric; 

Ionic;  Corinthian;  Composite:  Character;  Proportions; 

Uses;  Typical  Examples;  Parallel  of  the  Orders;  Columns; 
Pilasters;  Base;  Shaft;  Capital;  Architrave;  Frieze;  Cor- 
nice; Arris;  Entecis;  Triglyphs;  Metopes;  Volutes;  Modules. 
Proportion  of  Arches;  Doorways;  Pediments;  Windows;  Bal- 
ustrades; Colonnades  and  Arches. 

WORKING  DRAWINGS:  Details  of  Window  Frames  for  Brick 

and  Wooden  Buildings;  Details  of  Framing:  Floors;  Par- 

titions; Joists  and  Girders;  Sills  and  Posts;  Rafters;  Attic 
Floor;  Roof.  Dormer  Construction.  Tenon  and  Tusk  Joint. 

- Hanger.  Details:  Bulkhead;  Fireplace.  Details  of  Finish; 

Sliding  Doors;  Ironwork  in  Connection  with  Framing.  Details  of  Gutters. 

ARCHITECTURAL  DESIGN:  Utility;  Effect;  Unity;  Grouping:  Interiors;  Exteriors; 

Orders;  Moldings;  Greek  and  Roman  Moldings;  Pedestals;  Arcades;  Columns;  Pilas- 
ters; Imposts;  Balusters;  Doors  and  Windows;  Piers;  Capitals;  Spires;  Form  and 
Color.  Ornament:  Greek;  Egyptian;  Roman:  Byzantine;  Gothic;  Italian;  French; 
English.  Plans:  Rooms;  Stairways.  Entrance.  City  and  Country  Houses;  Office 

Buildings:  Light;  Heating;  Ventilation.  Churches  and  Public  Buildings. 

BUILDING  MATERIALS  AND  SUPERINTENDENCE:  Limes;  Cements  and  Mortars: 

Strength;  Proportions;  Data  for  Estimating  Cost.  Stone;  Granite;  Limestone; 
Marble;  Slate;  Testing  Building  Stone.  Brick:  Paving  Brick:  Fire  Brick;  Glazed 

and  Enameled  Brick;  Building  Brick.  Size;  Mortar;  Construction  of  Walls;  Hollow 
Walls;  Brick  Arches;  Brick  Veneer;  Fireplaces.  Terra  Cotta:  Composition  and 
Manufacture.  Durability;  Inspection.  Setting  and  Pointing.  Examples  of  Construc- 
tion. Iron  and  Steel:  Girders  and  Lintels;  Supports;  Bear- 

ing Plates;  Chimney  Caps.  etc.  Laths  and  Plastering.  Metal 
Laths;  Stucco.  Concrete.  Superintendence:  Necessity  for 

Superintendence.  Visits;  Setting  out  the  Building;  Inspecting 
Material;  Inspecting  Construction;  Costs;  Contracts. 

STRENGTH  OF  MATERIALS:  Stresses  and  Deformations:  Ten- 
sion; Compression;  Shear;  Factors  of  Safety;  Working 

Stresses.  Beams:  Simple  Beams;  Cantilever  Beams;  Re- 

actions; Bending  Moments;  Moment  of  Inertia;  Center  of 
Gravity;  Safe  Loads;  I-Beams;  Deflection;  Beams  of  Uni- 
form Strength;  Continuous  Beams.  Columns:  Cross-sections; 

Radius  of  Gyration;  Designing.  Torsion:  Shafts  for  Trans- 
mitting Power:  Combined  Stresses.  Testing  Timber,  Brick, 

Cement,  Wrought  Iron.  Cast  Iron  and  Steel.  Resilience: 

Sudden  Loads  and  Impact:  Elastic  Resilience  of  Beams. 

Tension,  Compression,  Shear  and  Torsion. 

FOUNDATIONS:  Staking  Out.  Excavation;  Loads;  Artificial 

Foundations;  Timber;  Piles;  Bearing  Power;  Cofferdam; 

Wrought  Iron;  Cast  Iron;  Blast  Furnace  Slag;  Retaining  Walls;  Concrete;  Mixing; 
Laying;  Compressive  Strength;  Period  of  Repose;  Variations  of  Proportions.  Shoring; 
Needling;  Bracing. 


■ KTAIL  • OT-  CCNttAL  • v/mcw  fXAH»J 


MASONRY:  Classes  of  Masonry;  Culverts;  Wing  Walls;  Pointing;  Grouting;  Freezing; 

Brick  Masonry.  Cement:  Hydraulic;  Natural;  Portland;  Characteristics  of  Portland 

Cement;  Testing;  Effect  of  Age;  Quick  and  Slow  Set;  Specifications ; Mortar;  Pro- 
portions; Sand;  Water;  Strength  of  Mortar ; Shearing,  Compressive  and  Tensile 
Strength;  Effect  of  Frost;  Permanency;  Data;  Specifications. 


CARPENTRY  AND  JOINERY:  Timber;  Shake:  Knots;  Quarter 

Sawing;  Seasoning;  Kinds  of  Wood;  Uses.  Framed  Structures: 
Joints;  Sills;  Posts;  Studs;  Bridging;  Flooring:  Par- 

titions; Lathing;  Trussed  Partitions  Roofs;  Jack  Rafters; 
Hip  and  Valley;  Mansard;  Gables;  Construction  of  Roofs: 
Shingles;  Flashing.  Balloon  Framing.  Siding;  Verandas; 
Arches;  Ceiling.  Joinery:  Joints;  Tongue  and  Groove;  Dove- 
tail; Dowel;  Mortise  and  Tenon;  Keys.  Interior  Work;  Wain- 
scots; Paneling;  Door  Making;  Sliding  arid  Folding  Doors;  Windows  Sashes;  Glass. 
Splayed  Work.  Bending  Wood:  Veneering.  Blinds;  Hinges;  Interior  Finish. 


STAIR  BUILDING:  Materials;  Terms;  Classification.  Construction:  Treads;  Risers; 

Stringers;  Steps  and  Platform;  Molding;  Balustrades:  Hand  Rails.  Straight  Stair- 

ways; Winding  Treads;  Winders.  Open  and  Closed  Stringers;  Curved  Stringers. 
Quarter-Turn  Winding;  Half-Turn  Platform.  Winding  Stairways;  Circular  Stuirwuya- 


541 


GRAPHIC  STATICS:  Force  Triangle;  Polygon;  Conditions  of  Equilibrium;  Stresses  in 

Truss,  in  Polygonal  Frame;  Reactions  of  Beams;  Concentrated  Loads;  Uniform  Loads; 
Overhanging  Beams.  Roof  Trusses:  Dead  and  Snow  Loads;  Stresses;  Wind  Loads; 
Fixed  Ends;  Truss  with  One  End  Free.  Abbreviated  Methods  for  Wind  Stress;  Com- 
plete Stresses  for  a Triangular  Truss;  Ambiguous  Cases.  Unsymmetrical  Loads  and 
Trusses.  Stresses;  Design  Plate  Girders. 

STEEL  CONSTRUCTION : Elements  and  Functions  of  Frame- 

work; Use  of  Handbooks;  Rolled  Shapes;  Tables.  Beams: 
Loads;  Effect  of  Openings;  Commercial  and  Practical  Con- 
siderations in  Design.  Columns:  Connections;  Shapes;  Se- 

lection; Calculation  of  Section;  Tables;  Use  of  Concrete 
Steel  Columns.  Trusses.  Types;  Determination  of  Loads; 
Shipping  and  Erection.  Details  of  Framing:  Connections  of 

Beams  to  Girders  and  Columns;  Plate  and  Box  Girder  Con- 
nections; Column  Caps  and  Bases;  Roof  Details.  Shop 
Drawings:  Processes  of  Manufacture;  Conventions;  Mill 

and  Shop  Invoices;  Checking;  Details  of  Work.  High  Build- 
ing Construction:  Steel  Skeleton;  Limiting  Heights;  Laws; 

Effect  of  Wind.  Portal,  Knee  and  Diagonal  Bracing.  Vibra- 
tion; Column  Loads.  Mill  Construction:  Requirements  of 
Underwriters;  Slow  Burning  Construction;  Steel;  Details  of 
Connections.  Types  of  Construction. 

FIREPROOFING:  Material;  Parts  to  be  Protected;  Choice  of  Material;  Use  of  Material; 

Floor  and  Roof  Arches;  Comparison  of  Terra  Cotta  and  Concrete  Steel:  Expanded 
Metal;  Tests;  Suspended  Ceilings;  Furring;  Partitions;  Column  Coverings;  Fire- 
Resisting  Wood;  Paint;  Metal  Coverings;  Relation  of  Construction  to  Architect’s 
Design.  Relation  of  Construction  to  Strength  of  Steel  Frame. 

CONTRACTS  AND  SPECIFICATIONS:  Classes;  Drawing  Up;  Seals;  Clauses;  Subletting; 

Assignment.  Failure  to  Complete  Work;  Insolvency;  Insurance;  Appliances;  Disputes; 
Condemned  Material.  Penalties;  Cost;  Monthly  Estimate;  Final  Acceptance;  Defi- 
nition of  “Engineer”  and  “Contractor.”  Specifications:  Forms;  Clauses;  Material; 

Workmanship;  Performance;  Specifications  for  Stone  Work;  Building;  Lumber; 
Cement;  Mortar;  etc. 

HEATING  AND  VENTILATION 

HEATERS:  Stoves;  Furnaces;  Steam;  Hot  Water;  Electricity.  Furnaces:  Location; 

Parts;  Direct  and  Indirect  Draft;  Pipes  and  Ducts.  Care  and  Management.  Ventila- 
tion: Carbonic  Acid;  Location  of  Inlets  and  Outlets;  General  Considerations.  Heat 

Loss  from  Buildings.  B.  T.  U.  Calculations  and  Tables. 

STEAM  HEATING:  Radiators;  Systems  of  Piping; 

Wet  and  Dry  Returns;  Valves;  Pipe  Sizes;  Indi- 
rect Steam  Heating:  Heaters;  Stacks;  Ducts; 

Wall  Box;  Care  of  Systems.  Exhaust  Steam 

Heating:  Reducing  Valves;  Grease  Extractor;  Ex- 

haust Plead;  Pumps  and  Traps;  Paul  System; 

Plenum  Method;  Efficiency  of  Heaters;  Fans; 

Factory  Heating;  Temperature  Regulators. 

HOT  WATER  HEATING:  Radiating  Surface;  Piping; 

Expansion  Tank;  Distribution;  Valves  and  Pipes; 

Location  of  Radiators.  Indirect  Hot  Water  Heating 
Sizes;  Care  of  Hot  Water  Heaters. 

VENTILATION  OF  BUILDINGS:  Choice  of  Systems;  Calculations,  and  Hints  for  Heating 

and  Ventilating  Schoolhouses,  Theatres,  Apartment  Houses,  Greenhouses,  Factories,  etc. 


© ° A 

bolts  spaced  2.'o  *, 

° ° 1 

COMPOUND -BEAM 

1 

Cast.  Iron  •Separators 
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I BEAMS  '"A  C l SEPARATOR 

n 

1 Top  and  bottom  plates 
I riveted 

1 BEAM  BOX  GKDER. 


PLUMBING 


FIXTURES:  Bath  Tubs;  Water  Closets;  Lavatories; 

Vents;  Connections; 


Bowls;  Sinks;  Traps;  Pipes; 

Sewers  and  Cesspools.  Plumb- 
ing: Connections  for  Bath  Room.  Kitchen  Sink 

Connections.  Plumbing  Dwelling  Houses,  Apartment 
Houses,  Railroad  Stations,  Schoolhouses,  and  Fac- 
tories. Testing  and  Inspection. 

DOMESTIC  WATER  SUPPLY:  Friction  in  Pipes;  Pipe 

Lining;  Pumps;  Hydraulic  Ram;  Kitchen  Boiler; 
Coils;  Water-Back  Connections;  Circulation  Pipes; 
Laundry  Boilers;  Boilers  with  Steam  Coils;  Tem- 
perature Regulators. 

SEWAGE:  Systems;  Considerations  Governing  Choice. 

Design  and  Construction:  Topography;  Manholes; 

Grades;  Flushing;  House  Connections;  Ventilation; 
Catch  Basins;  Pumping  Stations.  Purification; 

Sedimentation;  Chemical  Precipitation;  Irrigation; 
Intermittent  Filtration. 

GAS  FITTING:  Pipes;  Meters;  Fittings;  Joints;  Risers; 

Location  of  Pipes;  Testing  Gas  Pipes.  Gas  Fixtures: 
Burners:  Batswing;  Fishtail;  Bunsen;  Argand;  etc.  Chandeliers. 

Shades.  Heating  and  Cooking  by  Gas.  Automatic  Hot-Water  Heaters. 

Position;  Dials;  Reading.  Gas  Machines. 


Globes  and 
Gas  Meters' 


542 


uu/n/oj  cr/ow 


Roof  G/rcfer 


Defa/Z  of  Cannae  f/on  of 


flnee  Braces  fo  Columns 
ancZ  G/rders. 


/ 

\ 

\ 

/ 

/ 

\ 

/ 

/ 

Diagram  of  one  Column 
Bay  Braced  by  Knee 
P/ates  and  Angles  to 
resist  Wind  Pressure. 


TYPES 

OF 

WIND  BRACING 


Diagram  of  one  Column  Boy 
Braced  by  Porta/s  of  P/ates 
and  Anp/es  to  res/sf 
Wine/  Pressure. 


SPECIMEN  PAGE  FROM  INSTRUCTION  PAPER  ON  STEEL  CONSTRUCTION. 


ARCHITECTURAL  ENGINEERING 


INSTRUCTION  PAPERS  IN  THE  COURSE 


Arithmetic  (3  parts). 

Elementary  Algebra  and  Men- 
suration. 

Geometry. 

Mechanical  Drawing  (4  parts). 
Freehand  Drawing. 

Algebra  (2  parts). 

Perspective  Drawing. 

Mechanics  (2  parts). 


Building  Materials. 
Trigonometry  and  Logarithms. 
Strength  of  Materials  (2  parts). 
Foundations. 

Masonry. 

Statics. 

Steel  Construction  (3  parts). 
Fireproofing. 


CONTRACTORS’  AND  BUILDERS’  COURSE 

INSTRUCTION  PAPERS  IN  THE  COURSE 


Arithmetic  (3  parts). 

Elementary  Algebra  and  Men- 
suration. 

Geometry. 

Mechanical  Drawing  (4  parts). 
Working  Drawings. 

Building  Superintendence  (2 
parts). 

Strength  of  Materials  (2  parts). 
Masonry. 

Carpentry  and  Joinery  (2  parts). 


Sheet  Metal  Work  (2  parts). 
Metal  Roofing. 

Cornice  Work. 

Electric  Wiring. 

Electric  Lighting. 

Heating  a n d Ventilation  (3 
parts). 

Plumbing  (2  parts). 

Contracts  and  Specifications. 
Legal  Relations. 


CARPENTERS’  COURSE 

INSTRUCTION  PAPERS  IN  THE  COURSE 


Arithmetic  (3  parts). 

Elementary  Algebra  and  Men- 
suration. 

Geometry. 

Mechanical  Drawing  (4  parts). 
Freehand  Drawing. 

Architectural  Drawing. 


Perspective  Drawing. 

Building  Materials. 

Working  Drawings. 

Strength  of  Materials  (2  parts). 
Carpentry  and  Joinery  (2  parts). 
Stair  Building. 


ARCHITECTURAL  DRAWING 

INSTRUCTION  PAPERS  IN  THE  COURSE 


Arithmetic  (3  parts). 

Elementary  Algebra  and  Men- 
suration. 

Geometry. 

Mechanical  Drawing  (4  parts). 
Freehand  Drawing. 

Architectural  Lettering. 


Shades  and  Shadows. 
Architectural  Drawing. 
Perspective  Drawing. 
Rendering. 

Study  of  the  Orders  (3  parts). 
Practical  Problems  in  Design. 


544 


PARTIAL  LIST  OF  TEXTBOOK  WRITERS,  INSTRUCTORS,  AND 
EDITORS,  IN  THE  DEPARTMENT  OF  ARCHITECTURE 


WILLIAM  H.  LAWRENCE,  S.  B. 

Professor  Department  of  Architecture, 
Massachusetts  Institute  of  Technology. 

FRANK  A.  BOURNE,  M.  S. 

Architect,  Boston, 

Fellow,  Massachusetts  Institute  of  Technology. 

DAVID  A.  GREGG, 

Teacher  and  Lecturer,  Pen  and  Ink  Drawing. 
Massachusetts  Institute  of  Technology. 

H.  W.  GARDNER,  S.  B. 

Professor  Department  of  Architecture, 
Massachusetts  Institute  of  Technology. 

EDWARD  A.  TUCKER,  S.  B. 

Architectural  Engineer,  Boston. 

FRANK  CHOUTEAU  BROWN, 

Architect,  Boston, 

Author  of  “Letters  and  Lettering.” 

HERBERT  E.  EVERETT, 

Professor  Department  of  Architecture, 
University  of  Pennsylvania. 

CHARLES  L.  HUBBARD,  S.  B.,  M.  E. 

Heating  and  Ventilating  Expert,  Boston. 

EDWARD  NICHOLS, 

Architect,  Boston. 

GILBERT  TOWNSEND,  S.  B. 

With  Post  and  McCord,  New  York  City 

A.  E.  ZAPF,  S.  B. 

American  School  of  Correspondence. 

HERMAN  V.  VON  HOLST,  A.  B.,  S.  B. 

Architect,  Chicago 

ROBERT  V.  PERRY,  B.  S.,  M.  E 

Armour  Institute  of  Technology. 

EDWARD  R.  MAURER,  B.  C.  E. 

Professor  Department  of  Mechanics, 
University  of  Wisconsin. 

J.  R.  COOLIDGE,  JR 

Architect,  BostoD 


545 


SPECIMEN  PAGE  FROM  INSTRUCTION  PAPER  ON  THE  ORDERS, 


Man})  young  men  have  a wishbone  instead  of  a backbone.  " 


TO  PURCHASERS  OF  THE 

“CYCLOPEDIA  OF  DRAWING” 


struction  papers.  Our  object,  therefore,  in  publishing  the  “Cyclopedia 
of  Drawing”  is  to  enable  you  to  examine,  at  your  leisure,  the  character 


we  make  you  the  following  special  offer  : 

If  you  enroll  within  thirty  days  from  receipt  of  the  books,  we  will  include 
with  your  course  a set  of  our  new  twelve-volume  reference  library  “Modern 
Engineering  Practice,”  FREE  OF  ALL  COST,  as  an  additional  help  in  your 
studies.  For  description  and  contents  of  this  valuable  set  of  books  see  the 
next  four  pages.  It  is  the  most  simple,  complete,  practical  and  up-to-date 
technical  reference  work  yet  published,  and  is  alone  worth  more  than  the 
entire  cost  of  the  course. 

We  employ  no  agents  to  secure  new  students,  preferring  to  spend  the 
large  sums  necessary  to  pay  canvassers  in  building  up  that  part  of  our  school 
in  which  you,  as  a student,  would  be  most  interested,  namely,  in  main- 
taining the  very  highest  standard  of  instruction  that  it  is  possible  to  give  by 
correspondence,  at  the  lowest  possible  tuition  fees. 

Thirty  minutes  of  study  each  day  for  eighteen  months  should  enable  you 
to  qualify  for  a position  which  commands  at  the  start  $ i , 200  and  upwards  per 
year.  If  you  are  already  earning  this  without  a technical  education,  it  is  be- 
cause you  have  special  ability  which,  with  proper  training,  would  enable  you 
to  double  or  treble  your  present  pay.  It  will  cost  you  about  ten  cents  a day  to 
get  the  necessary  education.  Is  not  this  an  investment  well  worth  making? 

If  you  are  in  a rut  and  discouraged,  there  is  .all  the  more  reason  for  start- 
ing today  to  fit  yourself  for  more  congenial  work.  All  that  is  needed  is  the 
backbone  to  begin  and  to  stick  to  it.  Thirty  minutes  of  study  a day  will 
prove  an  investment  from  which  you  will  draw  interest  the  rest  of  your  life. 
Can  you  afford  to  pass  this  opportunity  by  ? 


AMERICAN  SCHOOL  OF  CORRESPONDENCE 


HE  “CYCLOPEDIA  OF  DRAWING”  is  compiled 
from  the  regular  instruction  papers  of  the  American 
School  of  Correspondence.  These  papers  are  not  for 
sale  to  the  public.  Experience,  however,  has  shown 
that  no  better  recommendation  for  our  school  can  be 
placed  in  the  hands  of  interested  persons  than  these  in- 


of  the  instruction  offered,  in  the  confident  expectation  that  you  will  de- 
cide to  take  a course.  As  a special  inducement  for  deciding  promptly. 


at  Armour  Institute  of  Technology,  Chicago,  Illinois 


“ Today  is  your  opportunity;  tomorrow  some  other  fellow’s.  ’* 


P?47 


' A machine  doesn't  need  brains.  A man  does.  You  must  be  a machine 


or  a man. 


REFERENCE  LIBRARY  MODERN 
ENGINEERING  PRACTICE 


IN  TWELVE  VOLUMES 


A Reliable  Guide  for  Engineers,  Mechanics,  Machinists  and  Students; 
Illustrating  and  Explaining  the  Theory,  Design,  Construction  and  Operation 
of  all  kinds  of  Machinery;  Containing  over  Six  Thousand  Pages,  Illustrated 
with  more  than  Four  Thousand  Diagrams,  Working  Drawings,  full-page 
Plates  and  Engravings  of  Machines  and  Tools 


PARTIAL  TABLE  OF  CONTENTS 

Volume  One 

Elements  of  Electricity — Current — Measurements — Electric  Wiring- 
Telegraphy — Including  Wireless  and  Telautograph— Insulators— Electric 
Welding. 

Volume  Two 

Direct  Current  Dynamos  and  Motors  — Types  of  Dynamos  — Motor 
Driven  Shops — Storage  Batteries. 

Volume  Three 

Electric  Lighting — Electric  Railways — Management  of  Dynamos  and 
Motors — Power  Stations. 

Volume  Four 

Alternating  Current  Generators — Transformers— Rotary  Converters— 
Synchronous  Motors — Induction  Motors — Power  Transmission  — Mer 
cury  Vapor  Converter. 

Volume  Five 

Telephone  Instruments  — Lines  — Operation  — Maintenance  — Common 
Battery  System — Automatic  and  Wireless  Telephone. 

Volume  Six 

Chemistry — Heat — Combustion— Construction  and  Types  of  Boilers — 
Boiler  Accessories — Steam  Pumps. 

Volume  Seven 

Steam  Engines — Indicators  — Valves.  Gears  and  Setting  — Details — 
Steam  Turbine— Refrigeration— Gas  Engines. 

Volume  Eight 

Marine  Engines  and  Boilers  — Navigation  — Locomotive  Boilers  and 
Engines — Air  Brake. 

Volume  Nine 

Pattern  Making— Moulding— Casting— Blast  Furnace— Metallurgy- 
Metals — Machine  Design. 

Volume  Ten 

Machine  Shop  Tools  — Lathes  — Screw  Cutting  — Planers -Milling 
Machines— Tool  Making— Forging. 

Volume  Eleven 

Mechanical  Drawing— Perspective  Drawing-Pen  and  Ink  Rendering 
— Architectural  Lettering. 

Volume  Twelve 

Systems— Heaters— Direct  and  Indirect  Steam  and  Hot  Water  Heating 
— Temperature  Regulators — Exhaust  Steam  Heating  Plumbing 
Installing  and  Testing— Water  Supply— Ventilation— Carpentry 


‘Next  to  knowing  a thing,  is  knowing  where  to  look  for  it. 


549 


“In  science,  read  the  newest  books;  in  literature,  the  oldest.  ” 


V is  the  man  who  has  learned  through  long  experience  and 
careful  study  who  knows  best.  Years  of  experience  in 
teaching  thousands  of  students  living  in  every  portion  of 
the  globe,  and  careful  study  of  existing  conditions,  have 
enabled  the  American  School  of  Correspondence  con- 
stantly to  enlarge  and  revise  its  work  so  as  to  make  it  best 
adapted  to  meet  the  needs  of  the  correspondence  student. 

The  text  books  of  the  American  School  of  Correspondence  have  been  pre- 
pared by  the  leading  college  professors,  engineers  and  experts  in  this  country. 
In  their  preparation  careful  study  has  been  given  to  actual  shop  needs.  Sim- 
plicity, brevity,  clearness  and  thoroughness  are  marked  features.  It  may  be 
said  in  this  connection  that  the  United  States  government  has  secured  the 
right  to  use  these  instruction  papers  as  text  books  in  some  of  its  schools. 
“Storage  Batteries,”  by  Professor  Crocker,  is  used  in  the  senior  class  work 
in  Columbia  University.  The  Westinghouse  Electric  and  Manufacturing 
Company  have  secured  a large  number  of  papers  to  be  used  in  their  educa- 
tional classes,  and  the  only  gold  medal  for  superior  excellence  in  Engineering 
Education  and  Technical  Publications  awarded  at  the  St.  Louis  Exposition 
was  given  to  the  American  School  of  Correspondence. 

There  has  been  on  the  part  of  the  school’s  large  student  body  a great  need 
of  a practical,  concise  and  thorough  reference  work — a reference  work  which 
would  supplement  their  studies  and  also  assist  them  in  the  solution  of  such 
problems  as  daily  confront  every  practical  man.  To  meet  this  need  the 
school  has  compiled  its  twelve-volume  reference  library  of  ‘‘Modern  En- 
gineering Practice.”  The  “Library”  is  edited  by  Dr.  F.  W.  Gunsaulus, 
assisted  by  a corps  of  able  specialists  and  experts.  It  covers  a broad  field  of 
engineering  work  and  includes,  in  addition  to  the  school’s  regular  work, 
many  special  articles  on  such  subjects  as  Wireless  Telegraphy,  Automobiles, 
Gas  Engines,  etc.,  thus  forming  a complete  reference  work  on  the  latest  and 
best  practice  in  the  Machine  Shop,  Engine  Room,  Power  House,  Electric 
Light  Station,  Drafting  Room,  Boiler  Shop,  Foundry,  Pattern  Shop,  Black- 
smith Shop,  Round  House,  Plumbing  Shop  and  Factory.  The  “Library” 
contains  6000  pages,  8x10  inches  in  size,  is  well  indexed,  profusely  illus- 
trated, and  substantially  bound  in  three-quarters  red  morocco. 


IT  FREE 

SPECIAL  OFFER  TO  PURCHASERS  OF  THIS  BOOK 

If  you  enroll  within  30  days  from  receipt  of  this  book,  in  any  of  the  courses 
listed  on  the  opposite  page,  we  will  include,  free  of  all  cost,  a set  of  the 
12-volume  reference  library,  “Modern  Engineering  Practice.” 


“Books,  like  friends,  should  be  few  and  well  chosen.  ” 


550 


The  world  pays  a salary  for  what  you  know,  wages  for  what  you  do.  ” 


COURSES  AND  TUITION  FEES 

DEPARTMENT  OF  ELECTRICAL  ENGINEERING 

Paid  in 
Advance 

1 $5.00 
a Month 

$3.00 
a Month 

Electrical  Engineering Reference  Library  (12  vols.) 

$52  00 

$65  00 

$72  00 

Central  Station  Work Reference  Library  (12  vols.) 

48  00 

60  00 

66  00 

Electric  Lighting Reference  Library  (12  vols.) 

40  00 

50  00 

55  00 

Electric  Railways Reference  Library  (12  vols.) 

40  00 

50  00 

65  00 

Telephone  Practice Reference  Library  (12  vols.) 

40  00 

50  00 

55  00 

DEPARTMENT  OF  MECHANICAL  ENGINEERING 

Mechanical  Engineering Reference  Library  (12  vols  ) 

52  00 

65  00 

72  00 

Mechanical-Electrical  Engineering. . Ref erence  Library  (12  vols.) 

52  00 

65  00 

72  00 

Sheet  Metal  Pattern  Drafting Reference  Library  (12  vols.) 

44  00 

55  00 

60  00 

Shop  Practice Reference  Library  (12  vols.) 

40  00 

50  00 

55  00 

Heating,  Ventilation  and  Plumbing..  Reference  Library  (12  vols.) 

40  00 

50  00 

65  00 

Mechanical  Drawing Reference  Library  (12  vols.) 

40  00 

50  00 

55  00 

DEPARTMENT  OF  STEAM  ENGINEERING 

Stationary  Engineering Reference  Library  (12  vols.) 

40  00 

50  00 

55  00 

Marine  Engineering Reference  Library  (12  vols.) 

40  00 

50  00 

55  00 

Locomotive  Engineering Reference  Library  (12  vols.) 

40  00 

50  00 

55  00 

DEPARTMENT  OF  CIVIL  ENGINEERING 

Structural  Engineering  Reference  Library  (12  vols.) 

60  00 

75  00 

85  00 

Municipal  Engineering Reference  Library  (12  vols.) 

60  00 

75  00 

85  00 

Railroad  Engineering Reference  Library  (12  vols.) 

60  00 

75  00 

85  00 

Surveying  Reference  Library  (12  vols.) 

40  00 

60  00 

55  00 

Hydraulics Reference  Library  (12  vols.) 

40  00 

50  00 

55  00 

Structural  Drafting Reference  Library  (12  vols.) 

40  00 

50  00 

55  00 

DEPARTMENT  OF  ARCHITECTURE 

Complete  Architecture Reference  Library  (12  vols.) 

60  00 

75  00 

85  00 

Architectural  Engineering Reference  Library  (12  vols.) 

45  00 

55  00 

60  00 

Contractors’  and  Builders’  Course. . .Reference  Library  (12  vols.) 

40  00 

50  00 

55  00 

DEPARTMENT  OF  TEXTILE  MANUFACTURING 

Cotton  Course Reference  Library  (12  vols. ) 

40  00 

50  00 

55  00 

Woolen  and  Worsted  Goods  Course..  Ref  erence  Library  (12  vols.) 

40  00 

50  00 

55  00 

Knit  Goods  Course Reference  Library  (12  vols.) 

40  00 

50  00 

55  00 

200-page  Bulletin  giving  full  description  of  the  above  and  50  short  courses 

on  request 

will  be  s 

ent  fret 

AMERICAN  SCHOOL  OF  CORRESPONDENCE 

at  Armour  Institute  of  Technology,  Chicago,  U.  S.  A. 

“A  man’s  brains  can  do  more  work  than  both  his  hands.  ” 


551 


Practical 

Lessons 

IN 

Electricity 


Compiled  from  the 
instruction  papers  of  the 
American  School  of 
Correspondence  and  pub- 
lished to  show  the  standard 
and  scope  of  the 
instruction  offered 


Storage  Batteries  (prepared  especially  for  home  studies  by 
Prof.  F.  B.  Crocker,  Columbia  University) 

Electric  Wiring  (prepared  by  H.  C.  Cushing,  jr.,  author  of 
“Standard  Wiring”) 

Electric  Current  (by  L.  K.  Sager,  S.  B.) 

Elements  of  Electricity  (by  L.  K.  Sager,  S.  B.) 

The  Scientific  American  in  reviewing  the  book  says:  “Practical  Les- 
sons in  Electricity  is  distinguished  by  a common-sense  treatment  of  a subject  which 
is  apt  to  confuse  the  student  not  a little.  Prof.  Crocker’s  wide  experience  as  a teacher 
is  apparent  in  the  division  on  storage  batteries.  That  portion  of  the  work  is  charac- 
terized by  the  lucidity  of  treatment  which  is  unfortunately  not  often  found  in  books 
on  this  subject.  The  division  on  electrical  wiring  is  a simple,  condensed  account  of 
what  a practical  man  ought  to  know.  A valuable  part  of  the  book  is  a series  of  prac- 
tical test  questions  pertaining  to  the  subject  treated.” 

American  School  of 
Correspondence  f“ihcNo°is 


552 


/ 


=====  CYCLOPEDIA  OF  — 

APPLIED  ELECTRICITY 


Five  Volumes— 2,500  Pages-Fully  Indexed -Size  of  Pace.  8x10  inches.  Bound  in 
Red  Morocco.  Over  ^.000  Full  Page  Plates.  Diagrams,  Tables.  Formula  . etc. 


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PRICE  UPON  REQUEST 


Some  of  the  Writers 

Prof.  F.  B.  Crocker,  Head  of  Department  of 
Electrical  Engineering,  Columbia  University. 

Prof.  William  Estey,  Head  of  the  Department 
of  Electrical  Engineering,  Lehigh  University. 

H.  C.  Cushing,  Jr.,  Wiring  Expert  and  Con- 
sulting Engineer. 

Prof.  Geo.  C.  Shaad,  University  of  Wisconsin. 

J.  R.  Cravalh,  Western  Editor  of  the  Street 
Railway  Journal. 

William  Boyrer,  Division  Engineer,  N.  Y.  and 
N.  J.  Telephone  Company. 

Chas.  Thom,  Chief  of  Qundruplex  Department 
Western  Union  Telegraph  Co. 

Prof.  Louis  Derr,  Massachusetts  Institute  of 
Technology. 

Percy  H.  Thomas,  Chief  Electrician,  Cooper- 
Hewit  Co.,  New  York  City. 

A.  Frederick  Collins,  Author  of  "Wireless 
Telegraphy.” 


Partial  Table  of 
Contents 

Parti.  Magnetism — Electric  Cur- 
rent — Measurements  — Wiring  — 
Telegraph,  including  Wireless 
and  Telautograph. 

Part  II.  Di  rect-Current  Dynamos 
and  Motors,  including  Types  — 
Motor  Drives  — Westinghouse 
Three -wire  System  — Storage 
Batteries. 

Part  III.  Electric  Lighting— R til- 
ways— Management  of  Dynamos 
and  Motors — Power  Stations. 

Part  IV.  Alternating-Current  Ma- 
chinery— Power  Transmission — 
Testing  of  Insulators. 

Part  V.  Telephony,  including 
Common  Battery  System  and 
Automatic  Telephone. 


AMERICAN  SCHOOL  OF  CORRESPONDENCE 


CHICAGO 


553 


Cyclopedia  of  Drawing 


New  Enlarged  Edition 
5,000  Sets  Already  Sold 


TWO  VOLUMES 

1,200  Pages,  1,500  Illustrations 

PRICE 


.oo 

By  Express 
Prepaid 


Payable  in  Small  Monthly  Payments.  Money  Refunded 
if  not  Satisfactory 


“Comment  and  Appreciation** 

H.  W.  Le  S0URD,  Instructor,  Milton  Academy,  says: 

“ * * have  decided  to  put  the  books  into  our  drawing  room  as 

reference  books,  so  you  will  find  check  enclosed  for  another  set.  ” 

BERT  P.  FAWNS,  Philadelphia,  Pa.,  says: 

“I  have  attended  an  art  institute  for  four  years,  but  from  all  my 
studying  there  I have  not  received  as  much  knowledge  as  from  the 
“Cyclopedia  of  Drawing.”  It  brings  the  student  in  touch  with  all 
kinds  of  drawings  and  plans,  and  teaches  him  the  little  things  necessary 
that  an  instructor  would  not  take  time  to  explain.  I consider  it  the 
best  work  of  the  kind  I have  ever  seen.” 

“ AMERICAN  MACHINIST,”  New  YorK,  says : 

“Without  making  invidious  comparisons,  for  all  the  parts  are  good, 
we  may  mention  as  especially  good  and  thoroughly  practical  the  chap- 
ters on  Machine  Design  and  on  Sheet  Metal  Pattern  Drafting.” 


American  School  of  Correspondence 

: Chicago,  Illinois  ~ nr 


554 


555 


| FOREIGN  STUDENTS 


